Its going to be hard getting a beater for that price. That money is in breakdown territory. Plan on wrenching or buy a little motorcycle. They get great gas mileage.
Does not have to be as gay as mine but at over 100 MPG, yes I said 100 MPG I will be laughing at you too. Plus it will do 65 MPH all day long. Had it since 1980. Its a 1974 Honda Trail 90 with a Lifan 140cc motor in it.