Inventory management:
Priority in order:
SMG and shotgun. Other weapons are helpful but not necessary to win.
Backpack and unloading vest.
Any kind of armor, along with armor plates.
Dr Jones and first aid kits.
Medical glue/bandages, then splints. Bandages stack most often increasing their slot value.
Clothes(to make rags) and rags, to repair the backpack and unloading vest, or stabilize.
Antibiotics or sorbent. You should only need 1 type if you manage infection well, they stack up to 10.
SMG ammo, then shotgun ammo.

Anything else is lower priority and a candidate to be thrown away to make space:
Batteries. Plentiful, more useful if you find an XTS rapid blaster to use them.
Food. This is plentiful if you take the raw diet.
Repair Kits. Plentiful and it's unlikely your weapons will break even once before you win or die.
Morphine & Naloxone if you don't have both. Takes two slots and you need both, easier to find a stack of 5 bandages.

Generally keep items of the highest priority and drop lower priority to make room. This means shotgun ammo can be ditched, as you generally find more than you need, although the Crash 17 burst shotgun can help fix that for you.
The best bonus starting items are the first aid kit, and the frag grenade.

Gameplay:
The quick slots you start with and from unloading vest are important for survival.
Put an item you can use from quickslot there, some examples:
Bandages, ammo for current weapon, first aid kit, grenades, antibiotics.
You can use these mid-battle to heal, reload quicker or throw a grenade.

When enemy throws a grenade, run until at least 3 tiles between you. This does not save you if its an incendiary grenade as they have a very wide blast radius, but it prevents you from being spaced by a frag grenade.
Grenades can be thrown over some obstacles, and you can shoot over some obstacles. Grenade throwing isn't 100% accurate and they can hit walls and bounce backwards.

You regen 1 health/turn as long as you keep food a little above 400.

Keep health above 100 in general. If you are in combat, keep health above 100 with first aid kits etc, or risk being killed on the next action. Demons, etc can deal over 80 damage in a single hit with high accuracy. It's better to use that first aid kit then risk being killed with an unused kit in inventory.

You can heal infection with antibiotics, sorbent, a charged autodoc or amputation. You don't get infected as long as you stabilize it immediately and check it again after 6 or so turns.

Bloaters(fatman) deal a small amount of health damage AoE when they die. It shouldn't cause wounds or deteriorate equipment.

All enemies become tougher (bullet sponge), more aggressive and ecolapse into demons more often at a higher Q-level.
Q-level rises over time and as you kill basic enemies.
Q-level drops when you kill an Ishkur Gaal(-300) or other demon(-50) or when you smoke(-100).
Since demons spawn more often at high Q-level, it will bounce around as you kill them but tends towards 600-1000 overall.

Press space to wait on spot. Press F to fire on a location.

Bonus survival mechanics:
You can swap a weapon from inventory faster by dragging it over the current weapon, then pressing Escape to dump the other weapon on the ground. This takes less in-game time than placing the empty weapon back in inventory.

Walls can be shot out, for faster navigation or to move around holes made from grenades.

Don't walk into barrels. Check the medical locker at the starting elevator of every run for 2 free medical items. Enemies can cause friendly fire.

If you sneak past the first few enemies, you might be able to keep the Q-meter lower temporarily. Killing them raises the meter sharply. Overall it's not a huge effect.

While there is no great need, you can unequip "glory" armor at the beginning to conserve it for tougher, later levels when your backpack is more full.

The army knife can be thrown at early "sleeping" enemies within 4 tiles to one shot them. This does not have much overall effect.
v1.3 update: The character who starts with the knife now starts with a less accurate pistol, making the knife throw much better than shooting by comparison. Time your knife throw when the enemy is resting, and find a better ranged weapon asap.

You can close a door on a female disfigured enemy with spikes for arms, and she might not be able to reopen it, because no hands. Likewise for dogs and bloaters. If a corpse is in a door way, it will block it from being closed.

The scanning machine can be used to find the exit. You can often locate the exit with the first tier object scanner by checking for 2 items that are around 4 tiles apart. It only costs 5 batteries to charge to the first tier.


Best in class weapons:
Crash 17 is the best shotgun, it fires in a burst of 3, with a wide spread. Great at point blank where the spread does not matter.
Course VKT is the best smg, it fires in a burst of 4, quickly depleting 9mm ammo. Great at long range since the range and accuracy are high.
The builder nail gun fires in a burst of 8. Using the nails up can save some 9mm ammo.
The xts-666 blaster is the best energy weapon I found. It fires in a burst of 3.