a) Hmmmm ... depends, is fighting the zombies fun and exciting or scary and nerve-rackingly tiresome?
b) Do you still remain as 'you' if you become a zombie, or do you become a mindless monster (by 'you' I mean you, plus the desire to consume human flesh)?
c) Depends what you mean by vital, my penis isn't very important without someone to have sex with, if it was a hand I wouldn't be able to fight off the zombies so I'd die, without a leg I cannot run anywhere so I would die. If it was a finger or an ear ... then I could live without it.
Well my answer is like this.
I chop off said appendage as long as fighting zombies is fun, I would become a mindless thing and lose all sense of 'me' if I became a zombie and as long as the appendage wasn't a hand or a leg/foot.
I would just become a zombie if I was still me, just with a newfound liking for brains, if fighting zombies wasn't awesomely fun (cause if it was then I would go on killing) and if the appendage was vitally important to my survival (foot/leg and/or hand/arm).
Basically, whichever option is more fun.