The Washington Metro is a gem - perhaps one of the most thoughtfully and coherently designed subway systems in North America. The underground stations are architecturally striking, albeit all rather similar.
Unless I'm forgetting one, there are two commuter rail services serving DC: MARC (Maryland Area Regional Commuter) and Virginia Railway Express. Both serve Union Station. Although they have pretty good daytime service, you'll be disappointed to find that most American commuter rail only operates in the weekday rush hours, with little or no service on some lines at the weekends.
For Amtrak, DC is a major hub - you have dozens of interesting long distance routes to consider trips on in addition to the NE Corridor. You should join the forums at
discuss.amtraktrains.com - a kind of US equivalent of these pages, I suppose, where there is a wealth of info on tap about routes to take. Also bookmark and watch the
Amtrak Deals pages, specifically the
SmartFares which are available to book on many routes every Tuesday - Friday for travel over the following three weeks.