First, do not bring a car into DC. Traffic is horrible and parking is outrageously expensive when you can find it . Uber is easy and cheap. ($50 from BWI into downtown DC for example, with most downtown rides in the $7-8 range).

I would definitely stay downtown where you can walk to many of the key attractions. As to rates and suites vs. multiple rooms, don't bother with generalizations. There are times when you can't find a room and times when you may think that you won't be able to find a room only to find great prices.

You just have to do the research. It takes time, but there's no better way.