You should save pretty much non-stop: Leaving Port, entering Port, before/after accepting a quest, etc.
For example, your reputation diminishes if you ask the local governor for a quest and then don't accept it, meaning if you want to just check what he offers but don't like it, it is best to reload.
Not to mention very buggy behaviour and frequent crashes - the Storm Engine this game is built on was first released in 2000 and it is a miracle that it runs as well as it does.

Finally, the Quicksave feature is known to cause issues, so it is best to save manually.

• The class of ship you can use without a massive stat-malus is based on your Navigation skill. Employing a Navigator officer will transfer their Navigation skill to you. The required amounts are (Can be check by right-clicking on the Navigation stat):
  6th class - 1, 5th class - 25, 4th class - 45, 3rd class - 65, 2nd class - 80, 1st class - 95
  If you are just 1-2 levels off the next class, give an Adder Stone to your Navigator by temporarily making him a Boarder and using the Exchange menu.
  You can still use ships of a higher class, but it probably isn't worth it. The same applies to other captains sailing under you, meaning Navigation is the most important stat for them.
  
  
• The vastly increased upkeep for higher-class ships also means that early on, you are likely better off with a lower-class one, even if it has less cargo space / Hull / Crew. In first line if you are still doing quests, rather than freeplay cargo runs.
  (Thanks to A_Pauaw for this hint.)
  
  
• Being overburdened also decreases your stats. Sell your massive, quest-obtained stacks of gems and other shiny stuffs to a Usurer.
  
  
• The final reason for an unexpected stat-decrease is if you are wounded, which is caused by taking a lot of damage in multiple fights in a short period of time.
  To fix it, just go some time without fighting, or spend time in the Brothel.
  
  
• Reputation is (almost) only important for Officer loyalty - if you do too many bad things (e.g. piracy), a good officer will eventually leave your ship when their loyalty bottoms out and you next enter a tavern, and vice versa.
  You can tell the reputation of your officer by their 'title', and it is rather easy to tell whether it is good or bad (e.g. a bad one is Bloody Murderer, a good one is Hero). The best is Ordinary Sailor, as those don't care either way.
  Generally, every generated quest in a non-pirate city - other than the kidnap quests - will give you positive reputation. Piracy and smuggling will give negative reputation. It isn't really about morals, only about obeying laws.
  
  
• Your officers will regularly approach you in taverns because they want to resign. You can't really prevent this. However, they will always agree to stay for a one-time fee by choosing the third option and then always the first options.
  If you are really tight on money (likely in the early game) you can save-scum this. It is a random chance whenever you enter a tavern on a new day, meaning if you re-enter after reloading, it likely won't happen again.
  
  
• Try to safe up for an 'Ordinary Map' as soon as possible - it can be bought from the HWIC in Willemstad, Curacao. That is the big, yellow building in front of the market with some soldiers standing in front of it. Can't be quick-travelled to.
  
  
• Strategic Goods (Shipsilk, Ropes, Ironwood, Resin) are used for upgrading ships and cannot be regularly bought anywhere. As such, it can be a good idea to store these in a warehouse, rather than selling them right away - a warehouse is only 777 pesos per month, which shouldn't be an issue.
  Warehouses are available at each of the nations' headquarters:
  Capsterville (Saint Christopher / France)
  Willemstad (Curacao / Netherlands)
  Port Royal (Jamaica / Great Britain)
  Portobello (Southern Main / Spain)
  In order to rent a warehouse, you need to enter into the SECOND room of the shipyard in question, which I didn't know exists for Real-Life years.
  
  
• Different Ports grant different upgrades, and all require a different Strategic Resource for it:
  +Speed or Wind Angle (Shipsilk) - Port Royal, Jamaica
  +Max Number of Guns (Resin) or Increased Tonnage (Ironwood) - Portobello, Southern Main
  +Manoeuvrability or Lower Crew Minimum (Ropes) - Capsterville, Saint Christopher
  +Hull (Resin) or Increased Max Crew (Ironwood) - Willemstad, Curacao
  Restore Max Hull (Shipsilk+Resin+Ironwood+Ropes) - Sharp Town, Isla Tesoro

This section only applies if you are playing in Story Mode! Exploration mode removed these level caps!
(Thanks to ShadeMeister for the info.)

• Do the 'Final Lesson' quests, and then the 'Dutch Gambit' quest chain before starting with free-play properly. This is because these will become permanently unavailable if your level is too high - although the Dutch path is always available for the Dutch Gambit and the other paths' level maxima seem to have been raised from what they were in Sea Dogs (I did the English path on level 17, used to be locked at 15+), yet I do not know whether the level requirement was scrapped entirely.
  For the Final Lesson quests, I can guarantee that all Level Requirements are still in place.
  
  For the Final Lesson, you must not have started the Dutch Gambit, you need to be at least Level 4 and at most Level 12 for the first five quests, and at most Level 14 for the last quest.
  Spoiler-free list of where (and when) you can acquire the quests, you will always be approached when landing during these times (order is irrelevant):
  08:00 - 15:00 in Basse-Terre (Price of Discretion)
  08:00 - 20:00 in Saint-Pierre (Resin Dogs)
  08:00 - 20:00 in Port-au-Prince (Grandee Albalate)
  10:00 - 16:00 in Tortuga (Just Like Home)
  08:00 - 21:00 in Capsterville (Prison Break)
  And the Final Quest after doing all the others is triggered anytime in Saint-Pierre.
  
  Once you have done all this, you can safely start the Dutch Gambit (i.e. getting the 'Dutch Gambit' Logbook entry) and, by all means, stop worrying, since no further quests within or after the Dutch Gambit have level requirements anymore.
  
  
• If you missed the Final Lesson either through over-levelling or starting the Dutch Gambit, don't worry. The rewards are nice to start out with, but by no means required and they will make no real difference in the mid-to-late game.

• The land combat tutorial sucks, yes. My general hints to get into it is this: Always press 'space' to block (this is basically free and doesn't even cost stamina), Attack with left-click on a high-balance and right-click on a low-balance weapon (you can also just check which of the two deals more damage). And whenever someone does a heavy attack (the one with the super obvious wind-up), just press 'C' to parry them.
  
  
• Per default, you shoot your gun with 'Q' and drink a potion with 'X'.
  
  
• You will miss pretty much every shot as long as your Accuracy Stat is low. That is normal.
  Just hire a Cannoneer with Accuracy of at least 50.
  
  
• By entering the "Deck mode" (Press tab while in a naval battle), you can manually aim and fire the cannons at the enemy ship, which will be far more accurate early on, in first line for grapeshot and knippels. You will probably need to experiment a little with where you have to aim though.
  (Thanks to A_Pauaw for this hint.)
  
  
• Early on, it is normal that you barely sink any ships. It is just more cost- and time-efficient to board them, and it is also normal to constantly have to replenish your sailors due to this.
  A good idea is to thin out enemies by shooting 1-2 salvos of Grapeshot at the enemy ship before boarding.
  
  
• Spend your Ship Ability Points on Navigation skills. The final Navigation Skill 'Scourge of the Seas' can only be learned by the player, and it makes pirates and patrols ignore you on the worldmap as long as you have a Class 4+ ship.

• This game is a remaster of Sea Dogs - if you want to google for anything, always make sure to check for Sea Dogs answers as well, since most things stayed the same!
  
  
• You can press 'R' to speed up the game x2 anywhere. With the + and - keys you can further fine-tune the game speed (up to 3x on land, 8x on sea, 2.5x on map)
  (Thanks to A_Pauaw for this hint.)
  
  
• You can save a lot of time by learning the shortcuts for travelling to certain locations on an island, rather than walking there or even using the Enter-menu.
  The default shortcuts are:
  1. Port
  2. Store
  3. Shipyard
  4. Tavern
  5. Town hall (Governor's Residence)
  6. Usurer (Bank)
  7. Church
  8. Brothel
  9. Port Authority (Harbour Masters' Office)
  0. Prison
  (Thanks to John Armfeldt for this hint.)

There are a few things that might occasionally pop up in old Sea Dogs guides (which are still a great resource) that no longer apply. I'll try my best to put them here.

• Manga Rosas no longer despawn - in Sea Dogs, whenever you leave an area that had a Manga Rosa in it without picking it up, and enter a new area with another Manga Rosa, the first one would despawn. This is no longer the case, and as such you can no longer screw yourself out of Manga Rosas now.

Thanks for reading, if you have any feedback or other tips I should help, leave a comment!