DO NOT USE AN AR-15 FOR AN APOCALYPSE GUN
USE AN M14 (or its civilian cousin, the M1A)
The AR-15 is an unreliable, under-powered piece of shit that should have never made it off of Eugene Stoner's drawing board. For an apocalyptic scenario, it offers no advantages over the earlier M14.
The M14 offers far superior stopping power, accuracy, and reliability for the negligible expense of two more pounds of weight and five more inches of length.
The M14 is a simple, reliable, easy-to-maintain design that field-strips for cleaning in seconds. It accepts the M6 bayonet (perfect for close-in zombie attacks) as well as the new Beta C-Mag 100-round magazines. The Sage Tactical Stock system can transform the weapon from an archaic but effective warhorse to a modernized zombie killing machine.
An ideal loadout for a zombie apocalypse would consist of a selective-fire USGI M14 rifle equipped with a Sage Tactical stock, with a foregrip to help control recoil. The USGI flash suppressor should be retained because of its integrated bayonet lug. Optics should be left up to the preference of the user, but iron sights offer a distinct advantage in a zombie apocalypse because batteries for electronic optics may be scarce, and the standard M14 iron sights are adjustable for both windage and elevation in addtion to being user-friendly. A flashlight should also be mounted on the 3 or 9 o'clock rails for night use.
The user should wear some sort of MOLLE tactical vest, possibly with ballistic plates and as many full, new USGI M14 magazines that can be carried. The M6 bayonet (which can double as a survival knife) should be carried as well. A new 1911-style pistol (preferably Kimber or Wilson Combat, but Colt's Manufacturing makes good ones as well) chambered in .45 ACP should be carried on a thigh or chest holster for quick, easy access, also with plenty of spare, brand-new magazines.
A lightweight backpack not to exceed 35 pounds should carry vital supplies such as food, water, and first aid to the user's preference. A 100-round Beta C-Mag for the M14 should be included in the backpack if weight and space allow it. A short, lightweight aluminium (Little League specs) baseball bat should be strapped underneath or on the outside of the backpack for easy access as a melee weapon. Failing that, a common hammer can be used.
M14 for most situations. M1911A1 for CQC/backup. M6 Bayonet for super-close quarters combat with the M14. Baseball bat/hammer for silent and/or individual zombie kills. That's it for weapons.
Most shotguns are designed for hunting and have limited magazines, in addition to being unsuited for rigorous apocalyptic scenarios. They are tricky to reload and while ammunition may be plentiful, you cannot carry that much on your person. Shotguns are handy and easy to use, but have numerous disadvantages.
Assault rifles are good for zombies but are underpowered for fellow hostile survivors. Most assault rifles are also unreliable compared to the M14.
Sniper rifles are heavy and inconvenient, and take a lot of practice to get good with.
M14.