A Zombie apocalypse, like "dead" zombies, are not possible, and even if they were they'd die pretty damn quickly without me having to do anything.
And a nuclear apocalypse? Well..
In an atomic holocaust, we're all pretty much screwed.
For a zombie apocalypse, we need to set some rules as to what we are dealing with. Are these classic George Romero zombies, or are these zombies track stars, and each and every one of them can take gold at the Olympics?
Zombie:
Weapons: I have quite a large collection of quality melee weapons, such as, knives, axes, spears, swords, polearms. Ranged = blowguns (not effective against zombies, but works for small game), bows, crossbows. Firearms = rifles, shotguns. (I had a nice Ithaca short barreled automatic shotgun, but some dumb ass thief stole it and if I ever run across that guy...). I would save the firearms for real emergencies, conserving ammo. I would also rely on 'fire' (fire good) and explosives. Defensively I would use barricades (eg Cheval de frise - spiked barrier - like we see in Skyrim,) traps, and 'kill' zones.
Fish and Game is plentiful in my area, plus just the other day I counted around a dozen edible wild plants growing in an open area on my land. I would work with my neighbors to protect our food source. Water is available via wells, plus I know methods of purifying contaminated water. I have several survival type handbooks, which I would review and allow others to study.
Nuclear:
Assuming it was not 'total'...Similar plan as 'Zombie', but I would need to construct a radiation fallout shelter quickly - probably something underground, dug in hard clay (lots of it near here) and lined with cinder blocks (which I already have).