If we're speaking realistically?
Crowbar, Molotov Cocktail (and enough ingredients to make two more), Swiss Army Knife, Duct Tape (silence is golden, duct tape is silver), and a bow.
Crowbars are fantastic. Not only will it legitimately pierce the skull of an oncoming zombie like it's nobody's business with utterly zero skill required, but I can use it to pry open locked doors, boxes, crates, and so on. Running out of food? No problem! Just go hit the nearest warehouse and use the crowbar to open all the crates till I find something to eat.
Molotov Cocktails are probably the best area denial tool I'd have that I could mass manufacture after the apocalypse. Plus I actually know how to make them. (Ethanol is your key ingredient. Beer doesn't make for a good molotov, but jack daniels? Vodka? Oh-ho-ho. Best ones you just empty the bottle and fill it with gasoline, but gasoline will quickly deplete and/or expire in the apocalypse.) If there's a swarm of zombies I don't care how shiny my weapon of choice is, the molotov will get the job done with greater efficiency in one toss and doesn't risk my ass in melee combat.
Swiss Army Knife, because can opener. And bottle opener. And screw driver. And so on. And it'll fit in my pocket.
Duct Tape, because you never know when you need to stick X to Y, or seal Z.
And a bow, specifically a mechanical bow, because I actually have taken archery lessons and know how to use it. Silent death at a range, with ammo I can retrieve from the bodies.
Throw in a backpack containing one of
these and I could even be happy in the apocalypse.
PS: Katana may not be the best choice of weapon in the apocalypse because it takes training to use properly and all it'll take is one screwed up swing to permanently damage your katana. It's definitely not the worst choice, but I'd saddle it somewhere in the middle. If I didn't have a crowbar or other type of bludgeoning multi-tool weapon around, sure I'd reach for it, but I'd probably more likely reach for something with a shorter, straight blade, so I can shank a zombie in the neck up into the skull, rather than trying to
decapitate it, because decapitations while pretty take a lot more skill and effort than a simple prison shank to the face.