Delaware is a bit too far for reserve because you either have to come through all the toll booths on 95 or come across the bay bridge. Either way you can get stuck for hours during the summer. Of course, you could always roll the dice and hope that you don't get a short notice callout.
There are basically two types of places to live around BWI, commutable to DC or not. Any place where people can commute to DC (Annapolis, Severna Park, Columbia, Laurel, Frederick, NoVA, etc.) is going to be considerably more expensive. Anyplace that's not convenient to DC (Harford, Carroll, or Kent counties, New Freedom, York, Gettysburg, etc.) will be more reasonably priced. Overall prices in the area have been going up 20% a year for the last five years so everything's pretty expensive.
I've flown with people that live in all of the above places. More people probably live in the Annapolis area than anywhere else but other than that everyone seems to be pretty spread out. I'd advise renting a place for a while to give yourself time to check out the area before buying. Besides, you'll probably need at least second year pay to qualify for the mortgage on most decent places.
As far as public transit, there's not much to speak of outside of DC's Metro. The commuter rail lines that go from DC to BWI/Baltimore only run M-F in the early morning and late afternoon. Baltimore's light rail goes right to the terminal when it's running (currently shut down until October), but it's just as quick to drive from anywhere north of Linthicum.