I'll chime in with another vote for light rail. Amtrak is more or less out of the question. If you were heading into DC, maybe. But light rail takes you directly from the airport terminal and deposits you in the thick of things downtown, for just a few dollars. The website with map and fare info is here:
http://www.mtamaryland.com/services/lightrail/
Keep in mind that airport trains only run every half-hour on Sundays, so be sure to check the schedule ahead of time.