You get the hats in the chest at the end of each stage.
I recommend in order:
Flamethrower Hat - Deal a lot of damage though move slower
Exploding Bomb Hat - Deals heavy damage though a projectile
Triple Shot - Slightly shorter range good damage
Black Hole Hat - Kills everything on screen(only take if you have a weak hat)
Ultimate Weapon Hat(Red beanie) Its not that strong and permanently reduces health to 1 heart.
Any of the protection hats(spike, water) - You just don't need them on easy. Though if you get a water hat drop on stage 3 you are probably getting the holy ship boss so grab it if you have a weak hat
I do a full run-through from about 12:30 in the video. The video is precisely how long it took for me playing for the first time to the 1000g completion.