Fast Pass will save you a couple of hours (depending on the time you leave).
You can get a Fast Pass through the Mass Turnpike.
The OP lives in Maine, so they should be able to get EZPass through the Maine Turnpike (if they don't already have it). (FastLane is the Massachusetts Turnpike's version of EZPass, but they work on each others' systems)
EZPass will get you through all of the tolls between Maine and Virginia, including the Maine Turnpike, the Hampton tolls in NH, Mass Pike, Tappan Zee Bridge (you'd pay coming home only), Garden State Parkway, Jersey Turnpike, the Delaware Memorial Bridge (Or the "Dell Member" as my family calls it), and the random toll bridge or tunnel going through Maryland.
Also, you can sometimes get discounted tolls using EZPass. I know that on the NY Thruway, EZPass users get a 10% discount on their tolls. I don't recall if this applies to the Tappan Zee or not. And starting 12/1, the NJ Turnpike is introducing discounts for EZPass users during off-peak hours.
Unfortunately, EZPass isn't accepted on any of the Florida toll roads, which all seem to have their own versions of electronic tolls. (And there's like three different ones!) *WHY* don't they get an agreement with EZPass???? I'm sure there'd be a lot of snowbirds that would be very happy if they did...
As for routing, I don't know the roads beyond DC, but my preference is 84 to 684 to 287 across the Tappan Zee. Then if I'm heading down through NJ I get on the Garden State Parkway. (sometimes I'm heading into Central PA or down to my parents in Shenandoah Valley, so I'd stay on I-287 around to I-78...)
-Rob