Congratulations on graduating and now being in the Air Force. My suggestions...
If you don't like getting up early, OR you just don't like driving, get a place AS CLOSE to where you work as possible.
If you DO enjoy getting up in the morning, and you don't mind driving and want some experience of the culture of the city...get a place as far away from it as you can stand (though you also should think about rising fuel prices).
Use the Air Forces moving resources, they actually are quite good. However, with DVD's, you might want to either take pictures of each and every DVD you have in their cases, OR put them in a carry case and carry them with you. You might also want to do that with games, and any real valuables (like Jewelry) that you have. It can work nicely, but you ALSO want to have someplace nice to go before you move. YOU might take a few days vacation to go to DC first and find a place, so you aren't living out of a hotel when you do get there...However, if you don't find a place, the movers should be able to put your stuff into storage.
Buy a GOOD cookbook and since you're int he military, you shouldn't have problems following the instructions (recipes).
Lots to see around the Local area of DC...that's a pretty big thing to cover.