OK I won three DC messenger races so I think I can comment here.
Rooms: My grandmother lives 10 minutes from DC by bike in Arlington. She has a cluttered house with lots of tennants. I lived there for 8 years. If you can deal with the clutter, the rent is dirt cheep and she has a room available. You can PM me about that. The only downside other than the above is that it is just a little too far to come home for lunch. When I lived in Adama Morgan I could go home for lunch, but the rent was about $700 more a month...
The only way to make real money in DC as a messenger is to have your own clients. The work is sporadic due to the Congress. In=busy. Out=slow. Bring a paperback with you. There are lots of companies, sometimes you can get a guarentee if you're experienced.
But you can do okay working for other people...You have to work hard and work long hours to make good money. Broadly speaking in addition to Bega Services/DC Courier, QMS (quick messenger service) is ok, although some people don't like the owner, and you have to do volume, but they have the work, ususally. Some people like Laser. Some like Apple. If you can learn to route yourself properly, and deal with free call, Washington Express is it. There are lots of other companies, I worked for Zoom for a long time.
The city is a grid, so you get the numbered streets and lettered streets right off the bat. The state streets, and the weird little one block streets can take awile, not to mention all the one way streets. But once you get that figured, you can move real smoothly. Get a map and keep it with you. After about three years, you won't use it much, but you'd be surprised how often you get an obscure address that you've never seen before.
It is a good town to ride fixed in, there aren't many or long hills. I rode 46x16 for a long time, now I'm more of a spinner and I'm on 44x17. Just don't lose your chain coming down Consititution on the house side.