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While it pains me to recommend a GW product, the only game like you describe that I can think of off the top of my head is Necromunda.

Not only do you arm your models as you wish (within certain limits provided by their list), but some people go so far as to name each member of their gang. It even has progression rules, so your models can get stat increases, new skills, permanent injuries, gain or lose equipment, etc.

It even sort-of takes place in an underground mine; specifically it generally takes place in the deepest pit beneath a Hive City where your gang fights other gangs to control territory in this region, called the Underhive, to salvage valuable scrap metal, mechanical parts, etc.

IMO, it's GW's best game.

Hm, I don't know a lot about Infinity, I didn't think there were multiple loadouts. I've heard nothing but good things about the game, so the OP might wanna go with that instead as it's more popular than Necromunda, and is actually supported by the company that makes it.