i know this in very detail cause ive done it before many times.
three airports in vicinity of DC. reagon national, dulles, and BWI. dulles isnt that close for me, so i usually use national airport because its two stops away on the metro for me.
BWI is great for cheaper flights. however its hour from airport to DC. if its a weekday yuou can take this shuttle that takes you to the marc train station. from there you can go to union station DC. this is okay, but its a pain in the ass if you haven done this before. (example..closed on saturdays and sundays) Also, if your departure flight is early morning you wouldnt want to do this.
the other option is airport shuttle from BWI to wherever you are going. there's a blue color bus called teh SuperShuttle. i dont know prices on that.
Id need more information to help you out further than this.