I'm setting a bit of a challenge for myself. It's too easy to get weapons and ammo from vendors, so I've come up with a challenge that makes good use of the crafting system and non-combat skills:
No buying weapons or ammo from any merchants, even caravaneers. Only looted or crafted weapons may be used. I may, however, buy crafting components.
No paying for weapon repairs. If it can't be repaired by the Lone Wanderer, it won't be repaired at all.
Armour may be repaired by vendors.
So far, my LW is doing pretty well, after a rocky start. Being a goody two-shoes, she tried to get out of trouble by surrendering her weapons to the Vault 101 Overseer, who then attacked her, forcing her to flee, lock herself in the Overseer's office and escape the Vault. Initially lacking anything stronger than a baseball bat, she acquired some decent hardware from Vault 106 and the Super-Duper Mart before finally buying schematics from Moira and slapping together some homemade weaponry to take to Minefield.