There's endless debate about this topic. You could visit a number of sites (
http://zombiehunters.org/forum is fun) and check out their "What one rifle?" threads, which come out surprisingly like our "What one knife?" threads here. There are the AK/AR debates (which read suspiciously like the chopper/bushcrafter discussions here), the "manly rifle" v. "poodle shooter" arguments, and the traditionalist v. modern disputes. However, Your emphasis on relatively short distance and low weight help simplify the question.
The short version is this - buy an AR-15, lots of mags and ammo. The AR platform is lightweight, as is the ammo (critical if you're carrying it). The modern rifles are very reliable and accurate. They accomodate every accessory imaginable (for ludicrous example, here's a mount for a Glock 19 -
http://www.fab-defense.com/en/categ...niveral-tactical-attachment-for-glock-19.html - insert "Pimp My Rifle" meme here: "Yo, dawg, I herd ya like guns, so I mounted a gun on yer gun so you can shoot while you shoot."). The ARs are also flexible, in that a user can change out barrels and upper receivers for different lengths and calibers.
More importantly for SHTF, ARs are the most popular rifle in the U.S. They are the duty weapons for almost all military and many - if not most - police organizations. Ammo, magazines and replacement parts are (and likely would continue to be) abundant. Familiarity with the AR system is therefore a useful skill to pick up.
This guy's put together a comparison guide for shoppers, and keeps it updated:
http://www.m4carbine.net/showthread.php?t=6642
His chart explains the desirable features of a quality AR, and which manufacturers have which features. Here's the chart:
http://spreadsheets.google.com/pub?key=pwswheghNQsEuEhjFwPrgTA&gid=5
According to that chart, one of the better bargains ("bang for the buck" - ouch) is CMMG. CMMG has been running something lately on their site called the "bargain bin" that might be worth looking into.
Have fun in your quest.