The quickest way to get good is to learn the shooting patterns of enemies and bosses. Bullet Kin shoot out single bullets, Shotgun Kin shoot out spreads of bullets, Blue Shotgun Kin shoot out two spreads of bullets, so on and so forth. Some enemies will also lead their shots relative to your position, such as Veteran Bullet Kin and Bullats.

You get a Master Round (+1 heart container) if you flawless a boss, I'm sure you know this. Don't be afraid to use your blanks on a boss since they get refilled next floor anyways.

The boss reward will always be a gun if you haven't picked one up on your floor.

For shortcut 1, try playing Hunter. She has a slightly higher chance to get keys than the other characters (5% roll on room clear for a random pickup). Also, her starting weapons are very good for dealing with floor 1/2 enemies and floor 1 bosses.

For the coins, you need to dodge well. Enemies that land a hit on you will not drop any casings, so if you get hit by a Gun Nut you're down 5-15 casings. If you flawless floor 1, you should be around 60-80 casings. Clearing floor 2 without being hit too many times should get you the casings you need.

EASIER WAY TO GET CASINGS, BUT SPOILER
There is a secret floor, the Oubliette, accessable from floor 1. To enter the Oubliette, locate a room with a fireplace and put out the fire with a water barrel or any gun that leaves behind puddles. Enter the doused fireplace, and press E. A secret room will be revealed on the map which contains a grate locked by 2 keys. This floor contains enemies somewhat harder than floor 2, but also give you the chance to get more casings and keys. The boss is pretty easy, though