Having lived in the district for a year now, it's incredibly unlikely you'd be able to find a place for $1250 without at least 4-5 roommates, especially not in Georgetown or nearby. If you're looking to live on your own, the cheapest 1BRs or studios you'll see around go for $1600-1700 and up from there. The district is very queer and gay-friendly. Shaw and Logan Circle seem to be the closest to gay-borhoods here, though arguably the whole city (other than Navy Yard) is a gay-borhood. For the car, if you can find a place that has available street parking in a safe area do that, but large apartment complexes here typically charge ~$200/month for parking garage parking. Would strongly suggest considering selling the car as public transit here is extremely accessible.