I prefer renting my place* in short-term (2-4 month) increments, although I know a lot of people prefer long term tenants...if you do want to try short-term first, if there are hospitals near you, I've had good luck with travelling nurses. They move from city to city depending on where there's a need and generally stay for a few months. Agree with getting everything in writing, though--I get a boilerplate rental agreement from the state and then tweak as necessary regarding payments, overnight visitors, parking, etc.
*Basement in my current residence that uses some of the same common areas, not a separate unit entirely.