These skills include:
Edged Weapons
Impact Weapons
Flail Weapons
Pole Arm Weapons

uses:
weapon skill is used in the calculation to determine hits vs misses in combat, for both offense and defense. Additionally weapon skills may be involved in some events including intimidating thugs and pole arms are used in a competition with passing knights. Some weapons have a minimum skill level, but being below this will just reduce your chance to hit with the weapon.

training:
weapon skills train quickly through use. Additionally if you have a party member with high skill and your Local reputation is very high you can hire guildmasters as trainers. Swordsmiths will usually offer training in edged, armorers will usually offer training in impact weapons.

notes:
if your weapon skill is much greater than that of your opponents they will almost never be able to hit you besides glancing blows. (which combined with armor often only do small damage to endurance) Therefor one of the most important skills to max out is your chosen melee weapon skill - though this will happen over time on its own through normal game play.

The best weapons in the game tend to be impact or edged depending on what qualities you are going for. Flail is probably only useful for very low strength characters, and polearm is good for weak characters that can attack from behind their tanks.

in character generation:
Melee weapon skills do not appear necessary to unlock any professions during character creation

Skill:
Thrown Weapons

Uses:
Determines chance to hit for thrown weapons, including potions.

Training:
train through using thrown weapons or throwing potions
Sometimes tutorship is offered by bowyer guildmasters if a member of the party has a high enough missile weapon skill and enough local reputation

notes:
thrown weapons are high damage, and fast (low reload), but low penetration and expensive. Thrown weapons benefit from strength and potion damage modifiers.

Skill:
Bow Weapons

Uses:
Determines chance to hit for bow weapons.

Training:
train through using bow weapons.
Sometimes tutorship is offered by bowyer guildmasters if a member of the party has a high enough missile weapon skill and enough local reputation

notes:
Bows all do the same base damage but offer high penetration choices. also their ammunition is recoverable and easy to come by in normal encounters. Bows also benefit from strength damage and potion damage modifiers. High quality bows are available in game, including a useable holy relic.

Skill:
Missile Devices

Uses:
Determines chance to hit for crossbows, arbalests, and guns.

Training:
train through using any missile devices.
Sometimes tutorship is offered by bowyer guildmasters if a member of the party has a high enough missile weapon skill and enough local reputation

notes:
Missile devices offer high base damage and penetration, but do not benefit from strength damage bonuses. High quality guns are available in game. Crossbows and arbalests use recoverable ammo, that is often not found in game encounters, and guns use ammo that is not recoverable.

in character creation:
no ranged weapon skills seem to be a prerequisite for professions in character generation.

uses:
This skill is used as part of the alchemy calculation when brewing potions. the calculation for success is transparent in game as the following:

100 + Alchemy Skill + Int + PhStone Quality - Formula Difficulty (magic number) = % to succeed

Additionally alchemy influences if you can find the astrologers in the crafts district, and how willing they are to interact with you. It also determines if you can find alchemy related things at university. Also it may come into play determining whether or not you succeed at using some alchemical potions in events, such as purifying altars and scaring off creatures, or distracting guards. (some potion events are 100% success rate however)

training:
Alchemy is easiest to train by employing a city alchemist as tutor, though this method isn't as fun or profitable as just pumping out large quantities of an easy potion at 1 per day.

in character creation:
alchemist and master alchemist professions are dependent on intelligence rather than the alchemy skill, but offer starting formulae and the ability to improve the skill quickly. Other professions that give starting formulae include Oblate.

notes:

• the barrier to finding alchemists varies from city to city, seeded by RNG, but smaller cities tend to have easier to find alchemists, and a skill of around 20 seems enough to find most alchemists, certainly its enough to find one to train you more.
  
• alchemy can be temporarily buffed substantially by saints for finding alchemists and brewing potions. The saints blessing last 24 hours from when invoked, so if you wait until the afternoon to invoke the saint you can use the blessing for two days in a row at brewing potions.
  
• though alchemy is more a perk of the game than essential to game play, it can greatly improve the gameplay of the party. healing potions are a huge boon to playability, and having everyone toss a damaging potion at a horde of enemies and watching them melt under the explosions is pretty fun.
  
• alchemy also offers the quickest route to wealth, as the only craft and profitable product in the game.

uses:

• determines (along with virtue) how much DF is recovered at midnight and when praying
  
• determines success at defacing alters successfully and calling forth demons, as well as one encounter where you are asked to take someones confession.
  
• determines how much virtue is gained when making a large tither to a city church (if tithe is big enough party members gain religion/30 in virtue)

training:
this skill can be trained up by getting instruction from monks, universities, or a brief lesson from wandering hermits.

in character creation:
a level of 15+ is required to unlock the abbot/abbotess profession.

notes:
this skill is very useful, primarily for DF recovery and improving virtue.

uses:

• determines if you are admitted to city monks and monestaries
  
• determines if you can invoke a saint
  
• modifies how much DF you need to spend to improve success at invoking a saint
  
• may be used, along with Speak Common, to determine if a travelling bishop will let you plead virtue to avoid tithing
  
• along with religion determines how much DF you recover when praying and at midnight

training:
many events offer a small chance to raise virtue, most of them saving people or helping other religious people, however there are many methods of note:

• if your religion is 30+ then donating a large amount to a city church guarantees an increase in virtue by religion/30
  
• if you can gain access to a cruel lord's castle, demanding he treat his people better is very likely to net a considerable improvement to virtue
  
• the Witches high sabbath offers many opportunities to improve virtue, most of them also require high Speak Common skill, but the improvement appears guaranteed upon success.

in character creation:
hermit unlocks at a virtue of 15+
knight unlocks at a virtue of 20+ (also dependent on last profession being noble)

notes:

• this 'skill' is vital to success at invoking saints, as every saint has a 'minimum' virtue to invoke them at all. Also getting it higher improves costs of invoking saints and recovery. Since saints offer the best method of buffing your party members and healing, they are going to be part of every party member, eventually.
  
• most monks/monestaries require around 20 virtue (or fame) to get in, give or take - seeded by RNG at game creation.
  

uses:
this skill determines success in many many interaction events with humans, from intimidating guards or thugs, to avoiding tithes and fees demanded while travelling, to talking with city alchemists. It is vital to the success of the party, but also very easy to train up, since it gets tested frequently. (However when interfacing with lords or townhalls, it seems less important than charisma.)

training:
this skill can be trained in almost every event where it is used. The most reliable way is to try and talk your way through city gates - both during the day and at night.

in character creation:
Speak Common doesn't appear to unlock any professions, and is easiest to raise in merchant professions

notes:

• this is the only way, short of invoking saints, to avoid bandits that are rushing you
  
• some encounters seem to use the highest speak common of only female party members to test success, so its recommended that you use a female character for charisma and speak coimmon tasks

uses:

• used in calculation for success at university
  
• some rare interactions with witches and demons indicate that you might be able to talk with them in latin to avoid combat

training:
The strait forward way of training this skill is via a monk or university tutor.
there is a single event within the storyline of the game that offers a substantial bump to read latin, which is tedious but repeatable.

in character creation:
this skill doesn't appear to unlock any professions

notes:

• one might envision this skill is useful for getting access to monks libraries or talking to alchemists, but neither seem to care about your ability to speak latin at all when it comes down to mechanics.
  
• all checks against this skill seem to fall well under where you can buff it with saints and are not terribly frequent, so training it up seems unnecessary. I'd list this as a near useless skill.

uses:

• a low skill adds flavor text to reading notices. notices always say the same thing: there's a fine for being out after dark
  
• the R&W skill is part of the calculation to getting admitted to libraries at university
  
• there are rare events that require that a party member can read

training:
R&W can be trained via monk or university tutor

in character creation:
the profession of clerk is unlocked at R&W of 15+ (alternatively if you are born 'wealthy') - clerk is a prerequisite for a couple other professions, like professor or physician.
the profession of Professor is unlocked at R&W of 20+

notes:
much like Speak Latin, events requiring R&W are so rare and the buff available via saints so substantial that it seems pointless to train this up, unless you do so in character creation to unlock clerk. I'd list this as a nearly useless skill.

uses:

• determine the skill of a city healer
  
• determine if a healer can train you (they wont train better healers)
  
• 'recover strength' option (in camp or residency) recovers based on highest healer skill in the party at a rate of healing/6. So to get to 2 you need to be at about 33 healing.

training:
does not train with use, so you have to hire a healer or university tutor.
there is an event at the high sabbath that can occasionally train healing, though its unclear why.

in character creation:
physician unlocks at healing of 15+ (if you've ever been a clerk)

notes:
this skill is pointless, and the reason why is because there's many many ways to heal in game:

• first and formost if you pay the daily rate for 12 hours at any inn (city or hamlet) you'll automatically regain 1 str and all your endurance. so that makes every ion heal at 2/day. while getting to 3/day takes a lot of training and its difficult or expensive to find tutors to get you there. so you can just spend time recovering at the inn for pennies.
  
• Then theres the expensive potion method - essence of grace - it wont cap out your strength but it'll get you 90% of the way there.
  
• And finally theres half a dozen saints that will heal you in full, some for only 50DF - and you will find DF can be much easier to recover at camp than strength. (and almost instant at a hamlet confessional)

uses:
they might as well call this skill lockpicking. that's what its used for, and how its trained. There are some options in dungeon puzzles to use artifice, but they are usually not the best option available. This skill gets you into merchants or bankers offices at night to rob them for fetch quests, it opens dungeon doors, and it unlocks locked chests. in knocker events you may need a substantially high artifice to get all the possible treasures. having lockpicks in the character inventory is required for any of these uses within a combat scenerio.

training:
you get a chance to raise your skill after every encounter or event where you use it, most repeatably at the marketplace at night you can attempt to burgle 4 different buildings: merchants, fugger, medici, and hanse. one of them will have a trap that permanently reduces charisma and perception. best to avoid that merchant if you are grinding them for skill - unless your lockpicker uses neither of these stats.
alternatively the tinkers guild is always willing to offer expensive training

in character creation:
this skill doesn't seem to unlock any professions. It is easiest to train in crafts professions.

notes:

• the mid-game and main quest can be pretty frustrating without adequate artifice - though some saints offer almost max buff to artifice - they seem unrequired since it can be trained.
  
• as mentioned above best to have your best artificer not use perception or charisma.
  
• make sure your lockpicker has lockpicks (available at foreign traders and pawn shops)
  
  
  

uses:

• success at any event that mentions sneaking, including most climbing events (there are a lot of these options in event screens)
  
• success at moving around cities at night while avoiding night guards
  
• saving the schrat from the wild hunt (the reward for which is the only way to permanently raise strength in game)

training:
The main way is to sneak past guards or try to leave the city marketplace at night without getting caught
Alternatively sneaking in a robber knights window, or sneaking up on huts in the woods.

in character creation:
stealth doesn't appear to unlock any professions

notes:
this one is vital to party success, especially because its necessary to permanently improve the strength of party members. its easy enough to train, even early in the game while you're grinding thugs.

uses:

• blend with crowds to gain or leave a city
  
• escape from guards
  
• convince city thugs not to attack you

training:
try to enter the city by blending with the crowd
trying to train it by leaving can reduce local reputation on some difficulty modes

in character creation:
Street Wise 10+ is required to unlock the thief profession

notes:
almost every instance where streetwise is used also either uses Speak common or offers a speak common alternative. There are more uses for Speak Common and more ways to train it that street wise, so street wise seems redundant and/or useless.

uses:

• running away from non-human encounters
  
• running away from peasants that want to sacrifice you to a dragon
  
• competing with a passing knight
  
  training:
  trained through use. the above mentioned dragon related peasant encounter is repeatable, otherwise it trains slowly through running from things. (as long as there's a horse in your inventory)
  note: running from the wild hunt doesn't appear to train riding
  
  in character creation:
  no profession seems dependent on riding skill
  
  notes:
  riding can be useful for getting away from wolves and boars and monsters and gargoyles, but is hard to train, and most of those encounters offer a wood-wise or sneak based alternative (wolves, and monsters, etc) with exception of boars - which give only an agility based alternative. This skill isn't strictly useless, but not investing in it won't really make a difference on game play. also in a pinch there are a couple saints that really boost this skill.
  Also one should note that horses are required and you can lose them in various events, including successfully running from tazerwurms.
  
  

uses:

• Avoiding wolves and other encounters in the wild
  
• Appears to play a roll in detecting ambushes in the wild, along with perception
  
• fast-talking with humans encountered in the wilderness (along with speak common)
  
  training:
  trained through use. try to avoid every encounter in the wilderness. notable using it to try to avoid the wild hunt will train it occasionally.
  
  in character creation:
  hunter unlocks at WdWs of 15+
  
  notes:
  This one is pretty useful but there's not much to do in terms of repeatable events to grind it up. besides triggering a wild hunt and wandering around hoping it procs.