Definitely 12 ga for the Zombies, although a case could be made for 20 gauge if you forsee an all day shoot of the fast ones.
A day of that and you can get a really bad shooting bruise with a 12 ga.
At least that’s been my experience.
I usually take zombies out with my .12 ga AND save my shoulder by shooting from the hip!
The one round that solves all problems is a fools quest (albeit a fun one)
If had to chose just 1 rifle, for a do it all I would lean toward the SKS, its simple robust and fires a decent .311 bullet. The weight of a a 120 grain standard 7.62x39 is not going to be much different than a .38specaial with 158G RN.
If you get a Yugo, it even has a gas cut off that would make it a bolt action. If you take out the gas piston it is always a straight pull bolt action of sorts.
Milspec Ball is ok for a lot of uses, but soft point or even cast or copper plated lead can be used.
Accuracy can be improved with optics or a better iron sight, it will never be a 300y MOA gun but at 100y its plenty accurate. if you get the right one you even have the bayonet for the “everything went so wrong” moment.
Change the stock if you want either classic hunting rifle or “draganov” or a pseudo m-16 or even a folding stock the choice is yours.. (the wood stock is not that bad but a rubber but pad to make it longer is nice)
if you go practice with stripper clips reloading can get pretty fast, not box mag fast but still pretty good. and they are cheap.
If you want to go rim-fire, they a good bolt action can be had with little cost if you go used, if new a bit more but a .22RF really needs to be put RIGHT wear you want it to be effective.