I want to play!
1- Right now I'm looking for my first sidearm in real life to purchase. Probably gonna land on either the Springfield XD or the S&W M&P. For doomsday purposes, you're looking at a 9mm for best results. It's the most common center fire ammo in the US, and when you're scavenging for bullets that means a lot.
2- A tough call if you're only going to carry one long gun, but I'd put priority on the 12 gauge shotgun. Ammo is heavy, but common, and very versatile. Self defense, zombies, hunting, etc. shotgun does it all. I like my 870 with a 26" barrel and an extended magazine. 8 in the tube + one in the chamber
(20" barrel shown)
3- Scrapyard dogfather. Indestructible, big, battonable, and holds an edge. Everything you need and nothing you dont. And it's easy to carry out of the sheath from the well placed finger choil at the base of the blade. If I'm bringing an axe (see four) I'm taking a smaller knife. I LOVE my scrapper 6 for that. If we're talking constant non-undead combat, I like the spyderco warrior.
Dogfather:
Scrapper 6
4- doomsday to me says zombies. In that event, I'm going with an aluminum baseball bad with 1/2" bolts through the end of it, sticking out only as far as the bolt head and nut. Light, weighted at the end, solid points of impact to fracture the skull and cause sufficient brain damage. Anything else besides zombies and I'm taking my granfors Bruks Hunters axe. Axes are versatile, and in a bushcraft based civilization chopping wood, skinning game, hammering spikes into the ground etc. can all be done with an axe.
5- AR-15 chambered to .223/5.56. OK, remember when I said the shotgun would be a tough choice as a primary long gun? That's cause the .223 ammo is lighter, with greater lethal distance, and can be found in any police station in the country, so scavenging is a viable option for obtaining more ammo here too. AK's and SKS's are fine guns that fire cheap ammo, but you gotta seek out enthusiasts to find it. There are just as many AR and M16 enthusiasts as 7.62 round enthusiasts out there, in ADDITION to the police that use it, so you it'll be easier to find than AK ammo. And it can double as a hunting gun for varmints (though there may not be much left without a 22lr conversion kit) and medium-small game.