Shop on the first floor will always have a key if you haven't found one yet, so always check it first so you can pick up a key for 25 brass.
Secret rooms are slanted towards sticking off of the dungeon map rather then being someplace interior, so better to check outer walls for them, especially the chest rooms.
Ammo drops are a separate roll from getting a generic item drop on room clear, and chances increase if you're carrying guns that use ammo and/or are empty, so don't be too afraid to use that shit.
Chest tiers go wood > blue > green > red > black. Wood chests are rarely worth opening unless you have a massive glut of keys or have the lockpick. If you open both chests on a level one will be a gun and the other will be a passive/active item. Bosses will always give a gun as a reward if you haven't found one that floor.
You can steal items from the shop if you have things that invis/conceal you, or with the grappling hook from very far away. Stealing more than one item almost always gets you caught and closes shops for that entire run. Also curses you, which isn't normally a huge deal.
Bullet idol shrine trades a heart for damage, always worth. The skeleton ammo shrine fills all guns at the cost of curse, always worth unless you're 100% full on ammo. Dice shrine is very random, but generally worth touching imo. Blank shrine spawns a chest for using a blank, but it's still often locked so use at your own risk. The gun knight shrine or whatever heals you at the cost of the gun you're holding, sometimes worth.
Enemies you get hit by in a room won't drop brass on death, so pay very close attention to the big enemies like gun knights or iron maidens to avoid taking damage from them, as they often drop 10+ brass on death.
Coolness is a hidden luck stat basically that affects item drops upon room clear and items that increase coolness tend to be quite good. Item drop chance (ammo/key/armor/heart etc at end of a room) also increases the longer you go without a drop as well as without getting hit, so taking less damage means more items in general.
The secret floor, the oubliette, is almost always worth doing, even if you have to skip both first floor chests to have enough keys, at least once you're good enough/confident you can kill the first floor boss with a starting gun. The additional rooms for item drop chance and brass pickups far outweigh the two key costs, plus it has 2 chests + possible special rooms and an additional boss drop.
Because of the oubliette I tend to favor the hunter as the "best" character, simply because the crossbow is more than capable of clearing the first floor boss flawlessly, which means you can always have the 2 keys required to get in to the oubliette. Dog finding items is just gravy really.
The 2nd secret room is generally only worth it once you're pretty good at the game, or have a very good room clear gun, as the floor is MUCH harder than the regular floor 3, and the boss there is one of the most difficult in the game aside from end bosses.