Note that the MARC trains do NOT run on weekends. Check the online schedule. It's a great service during the week but obviously no use on Sat/Sun.

As for renting a car, I'd skip it. Parking is a pain and very expensive. Once in DC it is very easy to get around using the Metro or a taxi. Taxis are cheap within DC itself; it's crossing the river to DCA (in Virginia) that increases the fare a bit (still not too bad). As stated earlier, you can take the Metro (BLUE or YELLOW line) to DCA. The Metro stop at DCA is right at the terminal so you will be off the train and at the security lane in less than five minutes.