As the resident expert what would you suggest?
It really boils down to proximity. If you are going to be fighting a zombie in close quarters than you want an instrument that can inflict maximum brain damage with minimum blood spatter. My recommendation would be a crowbar, as not only can it be a deadly weapon, you can use it to open doors that may be jammed or locked. Remember, the key to surviving the zombie apocalypse is to be able to hide effectively, run when needed, scavenge safely and outlast the zombie hoard.
For long range weapon you can never go wrong with a sniper rifle. Does huge damage when properly aimed at the head, without body parts flying around everywhere as possible contaminants. You have a long range and can easily take a high vantage point and snipe tonnes of zombies safely from your perch. It's also lightweight, easy to run with, can be used it closer proximity with less splatter than a shotgun. The ammo is relatively small and many rifles have cartridges than can be preloaded for a quick succession of shots.
It's terribly important that it's not just any old hunting rifle, but a sniping/precision rifle equipped with a high powered scope. Their range is significantly better and are designed to do maximum damage for extended periods of time.
I haven't tested either of these theories against actual zombies, but I have played Left 4 Dead on XBOX for hours and find the sniping rifle is indeed the best. As for knowing my close encounter weapons, again I have to cite the XBOX game Dead Rising where you can basically use any weapon you can find to save yourself and kill the hoard.
There is no doubt in my mind that these video games are an accurate portrayal of what to expect when the zombie apocalypse happens. You can never be too prepared.