Pretty much you are stuck with killing and looting to get money in the early game.

One point to make is that the craps table is not tied to to your luck of gambling skill, so if you know how to play craps you can do pretty well. I can usually win around 10K from the craps tables in about 30-40 minutes. Though this feels a bit like cheating.

Don't buy stimpaks unless the merchant doesn't have enough money to buy your heavy stuff.
General advice for getting rich is just following the story, explore new locations as they appear on the map, the later the new areas appear the more money and equipment you can get there by doing simple quests.
In later areas it's very easy to get rich and the best equipment can be found for free.
Don't use stimpacks, use your healing skills as often as you can, then rest until you can use them again.

Something that really annoys me about the game is, that there is hardly a sense of achievement. I am currently at level 6 and everything feels like a chore. If i encounter 3-5 Raiders, i'm getting killed for sure. The Pistol doesn't do more than 10 points of damage and all good weapons are way too expensive (not to mention the ammo prices). I don't expect to get a fancy energy weapon right from the beginning, but it's no fun to get whacked by everyone all the time.

If your feeling really vengeful and want to go outta your way you can also do the San Fran/Navarro run and come back in either Brotherhood or Enclave power armor with all the guns/energy weapons you can carry out and stomp a total mud hole in em,

Mind you, doing that will let you stomp a mud hole in pretty much everything you'll run into early on till you start derping around in the San Fran/ NCR area.

I would suggest getting your hands on a .44 revolver, it's quick (4AP to fire, 2AP with the right stats & Perks) it packs a punch and it's fairly cheap compared to most of the other guns in the game. The only downside is it's limited range. I usually have the .44 revolver in one slot and the hunting rifle in the other. You can get pretty far with this setup, I find that some of the "better" weapons don't do as well until much later in the game. I usually keep these two as my main weapons until I can get my hands on the H&K P90c and the Bozar.

The achievement comes later on, when you finally have gun skills and decent weapons and can butcher a group of 10 raiders just like that.

I think Unarmed+Jinxed character is a excellent build. You don't rely too much in equipment. So you may try that. Just don't forget to have luck 10. And you're a bit limited in the choice of NPCs (Sulik is fine, since he's unarmed/melee, but characters that use guns will destroy their own weapons in a unlucky turn).