Given that you set this up as a world-gone-to-hell, no access to parts, repairs, or new guns question, my picks focus on availability, reliability, and usefulness.
Heavy machine gun
Here's my list:
Beretta 92A1 (9x19mm)
HK MP5 (9x19mm)
M4 Carbine (5.56x45mm & .223 Remington)
M2 Browning (.50 BMG)
M40 [Accurized Remington Model 700] (.308 Winchester)
Remington 870 Marine Magnum [Nickel-Plated] (12 Gauge)
Ruger 10/22 All-Weather Stainless
Forced to go on the run, I'd take the Beretta 92 and the 10/22.
Forced to pick a single one, I'd pick the 10/22 and a handful of BX-25 magazines.
Beretta PX4 .40 S&W - Beretta 92FS 9x19 Para - Rock Island Armory GI 1911 .45 ACP - Colt 1968 Detective Special .38 Spc. - Ruger LCP .380 ACP - Daniel Defense M4V1 Carbine 5.56x45 - Alpine Industries M1 Carbine .30 - Steyr-Mannlicher M1895 8x56 - Ruger 10/22 .22LR - Remington 870 Express Tactical 12GA - 1943 Izhevsk Mosin-Nagant M91/30 7.62x54R