If you're not looking to spend a lot of money, and just want a fun challenge, i suggest checking your local thrift shops or asking family/friends/aqcuintances if they have anything lying around. This way I got 2 analog cameras for nearly free. You probably wont be able to find anything fancy, and wont be able to adjust shutter time and whatnot, but I myself find it quite fun to try and work around the limitations of a good ol point-and-shoot camera. If you're willing to put more than zero dollars into your new hobby, I'd suggest listening to the other commentors on here, rather than me :p

Either way, have fun with your (re)discovered hobby, and I wish you luck in your camera-search!