You could always search pawn shops for used handi rifles. I have paid as little as $120 for a 45/70. Shotguns are usually 50 to 100.
Most common caliber I find them in is 243.
Probably best source of info on handis is the graybeard outdoors forum. There is a good bit of traffic in the handi section and its classifieds. There are tutorials as well on fitting barrels if you decide to go used.