Several people I know swear by the Olympus XA, and it's one of the smallest ones out there. All of the Olympus Stylus series ones are great imo, but some are more expensive than others. I have the Olympus Stylus Zoom 140 which seems to be pretty cheap and reliable. A friend of mine has the Olympus Infinity Stylus that we both love.
Honorable mentions: Pentax Espio 140V and the Fuji DL-150
Itโll run you ~$100 but I love this point and shoot, and it doesnโt require batteries! But film is expensive. Iโd recommend sticking to Kentmere B&W.
Digital is 100% cheaper but I donโt have good inexpensive suggestions. I go all in on the highend ๐ You could always try to find my first ever camera: the Kodak MC3