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; 92FS; 92S; 8040G | Rock Island GI 1911 | Sig Sauer SP2022; P6 | Colt Python 4"; 1968 Detective Special 2"| Smith & Wesson M642 No-Lock | Ruger LCP; 10/22 | Daniel Defense M4V1 | Remington 870 | Alpine M1 Carbine | Steyr M1895 |1943 Izhevsk Mosin M91/30