Getting decent equipment in the game can take a while... the combat encounters are tough, and there tend to be 3 or 4 enemies who gang up on you at a time. Not a promising situation, to say the least.
In order to get enough money to purchase some more firepower, it's worth taking Steal as one of your tag skills. The first few times you gain levels, pump most of your skill points into Steal, until you get it around 60% or so. Then, you can wander around the various cities (the Hub is an excellent choice), stealing all that extra ammo that people are carrying. Save your game first, and if your steal fails, restore. Interestingly enough, you can steal from everyone in the game and it won't lower your Karma score. And in fact, each time you successfully steal something, you get a few experience points to boot. Not a bad deal!
When you've collected a good bit of extra ammo (and some folks even carry extra weapons), you can cash them in at your nearby weapons store. Something neat about being level 3 and having a bankroll of 20,000 caps.
Note that it can also work to your benefit if you later decide to attack the folks whom you have stolen from... no extra ammo means that they can't shoot at you as often as they'd like.
A related tip (no extra charge): If you run a merchant out of bottle caps, simply end the barter session, then talk to them again. Voila! A new bag of caps will magically appear.