No worries! : ) I'll actually be moving to D.C. from Seattle and I'm so excited to tell people that I'm from the "other Washington" ; )
To the original poster, I actually interviewed at CNMC and they offer $25 + $2 if you're working in PICU/NICU (I'm in the NICU), plus $3,000 bonus. No relocation bonus, I don't think. Plus shift differentials which someone posted somewhere around here but it's something like $3-4 for weekends/nights.
For housing, Craigslist is the king of everything in the world of moving. Supposedly for dating as well, but I haven't tried it

In any case, you can click on the Wash DC link, and search for apartments there (rooms/shares). As a cautionary word, you probably won't be able to find anything unless you're 2-4 weeks out of actually moving into a place. Do you want to live with roommates? D.C. is a very transient city with "young professionals" coming and going all the time, so I'm hoping to live in a group home with some folks. I think that's better than just getting one roommate with dynamics, but that's just me : )
The metro is pretty awesome--not as fabulous as NYC, but still gets the job done. I'm bringing my bike and I hope to just use that + the metro. Maybe get a vespa!
Hope this was helpful!