Just tried this game, its fun but I HATE the ridiculously low amount of ammo.
Unless you are doing some gimmick build speccing full into more ammo mutations is just a no-brainer and even then its very possible to run out even when not spamming bullets.
What you want to do is combine a sustainable weapon with a burst weapon. Crossbow is sustainable, it can oneshot enemies all the way till the last area; if you use nothing but the crossbow you'll never run out of ammo. Unless you miss but even 50% hits should be fine as long as you get close enough to pick up ammo when you see it. But when you spawn in front of 20 crows or snowbots a crossbow just isn't going to cut it, so you need to combine it with a weapon that lets you go all out and hold down RMB till everything is dead.
Examples of sustain weapons: Revolver/MG, crossbow, slugger, grenade launcher, lightning rifle, bazooka, any ordinary melee weapon.
Examples of burst weapons: Revolver/MG/AR, Pop gun/rifle, disc gun, laser pistol, auto shotgun/crossbow, minigun, anything with "cannon" or "super" in the name.
You'll notice all the the sustain weapons are pretty low level. Some of the later ones work as sustain, but only with mutations. Heavy bullet weapons work with recycle gland, gatling slugger/bazooka work with eagle eyes.
Another trick you can do is alternate between weapons often, the game is designed so you naturally lose ammo in weapons you have and gain it in weapons you don't have.