If you're new to the Virginia/DC climate, I'd recommend a peacoat (I don't have any particular brand recommendations) , certainly one that covers the rear. Ideally, you'd have two--a mid-length one for everyday and a longer one for more formal wear... Stock up on cute scarfs to go with!
Also I'd get a snow jacket of some kind for rainy days and/or weekends. North Face, Columbia, something like that.
I also have a lot of cardigans for the inbetween times. But that's because I have a cardigan fetish LOL.