Seeing this pop back up made me rethink a little bit, especially the post by Bullseye. Who says you NEED a GUN for person protection. Being on an extremely limited budget basically rules out the practice that is required to maintain a proficiency with a handgun. OUT! Shotguns, at close range, are basically large bore rifles that require practice to use effectively. Not as much as a handgun, but the budget is tight, so nearly any practice is OUT.
What about a good length of stick? A 4-5' long walking stick is a nasty weapon at close range. Give a 'bore' diameter of 1-1 1/4" and the caliber is just about right for most 2 legged predators and the price and cost of 'practice' fit right in the family budget. A short walk in most wooded areas will turn up just the right thing. Saw the ends somewhere close to square, if you want to get fancy, install a wrist strap made of old shoelace and you're out $.10 maybe, since you were probably going to pitch those old laces anyway.
I'd rather have a .357 or a 12 gauge, but I also shoot a lot and hunt, wo use of those weapons comes pretty easily for me. If I had to live under the original constraints, I'd get a stick. At extremely close range it can disarm most 'gang-banger' type assailants with ease. A trained opponent would be a more difficult target, but how many street punk train and practice?
Plus, it's legal to carry in the street without a permit or holster. And I think that it's legal in all 50 states, so the grabbers haven't gotten to sticks YET!