First rule to zombie killing / hunting dont make to much noise they track noise--hence the supressed part
I suggested
.22lr pistol, semi-auto
.22lr scoped rifle
AR 15 style rifle (large calibers are not condusive to zombie hunting why you ask?
large caliber hand gun (incase you get bit its best if you just take yourself out)
Large caliber rifles are out, why?
1. to much bang (remember zombie flesh is slowly deteriorating and it wont take much to penetrate it.)(over penetration can be very bad, you could make more noise using a supressed .308 and some over penetration than a supressed .22lr.)
2. splatter damage (you dont want zombie blood on you)
3. less is more (your gonna have to burn the bodies you dont want to pieces spread everywhere.)
4. you can carry more ammo (in a class 3 -5 you are gonna encounter a lot of zombies especially in a urban / suburban area and your gonna need a lot of ammo) if you dont have a large caliber
.22LR will allow you to carry enough ammo and a lot of loaded magazines, and its especially easy to find, 500 rounds per box say perhaps 5 boxes should allow you to hunt zombies pretty efficiently, remember its not necessary to blow their heads off especially if you are using varmint rounds you ought to be able to get some decent penetration in a head shot.
Your weapon type is also determined by what you are going to be doing are you going HUNTIN or is this primarily so you can get the hell out of dodge!