Well the VP70 isn't a pistol that's widely recognized, I'd imagine that's one reason he chose it. It looked (for the time) different enough to be a futuristic service pistol. I'm assuming it's USCM issued since Goreman is the only person we see with one.
Hick's shotgun was a personal weapon, that's something (based on dialogue) we can figure was personally owned by him. It wasn't a USCM issued weapon. I'd imagine the USCM issued shotgun would look more in line with the pulse rifle.
Vaz's pistol you can argue is also a personally owned weapon given the fact it's different from Goremans and can be easily identified.
Since these weapons are their personally owned weapons that means they were purchased via civilian means.
In keeping with the Vietnam logic though, it wasn't uncommon for soldiers to get weapons through unofficial channels or by family members sending them through the mail. I've read this was most often knives and smaller things, but in rare instances I've read WW2 weaponry could be acquired. Large weapons being sent to troops though was a common among snipers more so since the US Military didn't have an official sniper rifle during the beginning of the war. Personally owned or purchased hunting rifles were very common in the beginning of the war.
I know it's Ridley's movie, and I know he doesn't really have to follow anything after Alien, but keeping things a little bit in what was already established would be nice, or at least disguising the weapons a bit so they don't look like something you'd see a US or Australian military member with. It comes off as lazy to me.