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 Type F Fullsize .40 S&W | Beretta 92FS 9x19 Para | Beretta 8040 Cougar Type G .40 S&W | Rock Island Armory GI 1911 .45 ACP | Sig Sauer SP2022 Stainless 9x19 Para | Sig Sauer P6 9x19 Para | Colt Python 4" .357 Magnum | Colt 1968 Det. Spec. .38 Spc. | Ruger LCP .380 ACP | Daniel Defense M4V1 5.56x45 | Alpine M1 Carbine .30 | Steyr M1895 8x56 | Ruger 10/22 .22LR |1943 Izhevsk Mosin-Nagant M91/30 7.62x54R | Remington 870 12GA