Getting through immigration and customs at IAD with Global Entry is really, really quick. If you don't run into any problems, you can be outside the terminal 15 minutes after you walk off the plane.

A cab from IAD to DCA will be about $70 or so, and should take less than an hour, probably closer to 45 min, depending on traffic on I-66.

The Washington Metro goes right into DCA but not IAD. There are a couple of options to connect to the Metro from IAD. See http://www.wmata.com/getting_around/new_metro/. All of them are going to take some time, and honestly if I were flying in on an international flight, I'd bite the bullet and spring for a cab.