DK,
Do you plan on taking the scanner around with you or just sit and listen to the airport? Reason I ask is that you can buy a mobile or desktop scanner which has a considerably better audio output than handhelds.
If you want to carry the scanner around with you, then go for a handheld.
All the current scanners on the market have an 'aircraft' search band for the VHF (commercial) aircraft frequencies. The DB here can give you specific freqs for National.
That said, what else, besides ATC, do you want to listen to? A vast majority of the public service systems in Norther VA and DC are digital. So if you want to monitor Alexandria, you will need a scanner with a digital capability. The best ones on the market right now are Uniden's 396/996 and GRE's PSR500/600 (first number is handheld, second is mobile).
There will be some argument on this, but for sheer number of systems in the NOVA area, I'd recommend the Uniden over the GRE. The GRE is newer (came out late last year) and has some nice 'bells and whistles', but twenty scan lists on the GRE versus 99 user accessible banks on the Uniden's could easily be a deciding factor.
You might want to look through some of the threads in this and the Uniden and GRE radio forums to get some familiarity with what each of these scanners can do. A lot has been written on all of them and there are folks out there who will swear by one or the other.
These scanners also allow you to monitor MILAIR (which can be active around the DC area). Check the military forum for info and some links on this.
Good luck in finding a scanner and welcome to Radio Reference.