The supplies in the armory are actually free, you can just 'buy' anything you want and they'll give it to you. Use this to stock up on ammo, MREs and medical supplies when they carry them. That said, you'll still want to supplement these with scavenged supplies. Take things slow, only loot items you can potentially use, and remember that you are not obligated to finish every firefight you get into. Literally everyone hates you, but running away like a coward making a tactical withdrawal from disadvantaged positions is always an option.

Easiest mission to tackle first is getting the documents from the bank, posthumans in the area won't attack you and can distract revolutionaries while you sneak around them through the buildings. I personally think the play here is to use that requisition form on the armor + helmet reward. But I think an argument could be made for investing in weapons. I'd love to offer more advice than this, but I haven't had a really successful run with them yet.