Dys, that's great for your students, but they didn't get there without you at the helm.
I'd pass on renting a lot with a price which cannot be fixed. If I were in your shoes, my toes would be screaming I'd certainly get a realtor to show me very small houses, explaining what other features besides size are important (charm? storage? updates? location-location-location?). If you lived here, you'd have many pre-war choices, one- and two-bedroom homes so small few people want them. (Even people living alone want more space than previous generations needed to raise their families.) Many would need updates in kitchen and bath, which last saw improvements in the 1960s or 70s, but the selling prices are often so low you could afford that in due time, and they're fully functional now.
Another thing to look into is purchasing a small lot in an existing neighborhood. Even towns like mine, fully developed since forever, have the occasional small lot on the market. Most builders don't consider them worth the bother of constructing a small home, because so few people want that.
But you do! Take walks and drives and see if there isn't a half-lot gone to weeds or trees right in the middle of some neighborhood.
Maryn, on her second load of laundry