Metro stations have fare card machines just inside the gates but outside of the... well whatever the hell those things are that have a 50/50 chance of closing up on your nutz.
There's two prices- one for non-rush and one for rush hour. All prices are from that station to the one you are heading to.
As far as parking- well it's all over the city. Lots of it too, but if you want to come back to a vehicle that isn't stripped and/or in flames.. then you are pretty limited.
The areas around the mall (a huge grass area that has trees on either side and is located between the white house and the wash monument) has free "3 hour parking" during the weekdays. I call it "free all day parking if you get there at 9:30AM". They never ticket for not moving, but they will ticket if you leave your car too early. Only happened to me once and I leave it there too early all of the time.
But in terms of accessibility, metro transit is the best. They have stops all over that get you to a lot of places- especially on the mall. Navy/Archives will put you out at 7th and Penn in front of the National Archives. Smithsonian exit will put you on the mall (if you go out the right exit)... which is also where the Smithsonian Air&Space is located.
Basically all the worthwhile stuff (aside from Washington's home.. whatever it's called) is easily accessible by metro. I'm not actually sure if Washington's house (or whatever you want to call it) is accessible by the metro train, maybe by metro bus.
So if you take a bus up here, get a place in Arlington VA, Roslyn VA, or Crystal City VA (near the Pentagon) and use the metro to get into and around DC.
If you drive up, do the same thing unless you don't mind driving around looking for parking.
You're coming on the weekend, though, I suppose... so your best bet is to use the metro.. and if you bring your own vehicle.. use that for getting to places outside of/around DC.
-SW