Remember that the MARC doesn't run on weekends. Also remember the new bus from BWI terminal to Greenbelt Metro. These are the best ways to get to DC from BWI. If you're coming into BWI from out of town, don't bother with a car until later. You'll just have to park it, and won't need it for DC as you've apparently already figured out.

If there's another reason you need to park a car (such as someone locally is picking you up, or you're meeting someone who is driving), then the best place to park is the BWI Rail Station. From there, you can get right on the MARC train. Or you can go back to the terminal and get that bus to Greenbelt Metro. MARC info at
http://www.mtamaryland.com/ Metro info (including the bus, which is run by them) at
http://www.wmata.com/ The garage at BWI Rail Station beats the satellite parking in price and usually in convenience, too (plus it's covered!)