This may seem obvious - but timing your visit to DC is a critical part of planning. When Congress is in session there are lots of folks visiting for business and the hotels tend to be expensive. When Congress is quiet DC is quiet. I went at Thanksgiving one year and stayed in a suite at the big Hilton near the White House for about $50 a night.

If you want to visit Congress there us a Hyatt on New Jersey but that is the less interesting end of the National Mall. I prefer the Hyatt near Chinatown.

I use the Metro exclusively - I've never had a problem. Fly into DCA. BWI adds a train ride - not a big deal but will add about an hour total. I dislike getting to/from IAD - but - if you like airplanes - consider IAD because the Smithsonian museum is there - the Air & Space Museum on the Mall is small - rhe one at IAD is huge and worth he trip for aviation enthusiasts.