I rode the whole thing in May of 2012, shortly before moving out of VA.
To get maximum mileage, I started at the North end of the Great Falls National Park and rode through the park to connect with the north end of CCT. I took it all the way down to the southern end and finished by adding on laps around the loops at the Laurel Hill area, again extending mileage.
You can cut off the two ends and just do the CCT proper or just link together as much trail as possible.
Since my goal was to maximize true singletrack, I also took a few detours along the way, hopped off the CCT to hit the additional ST and hopped back on afterwards. I hit additional singletrack at Lake Fairfax, Colvin Run, Colt's Neck, Fox Mill, Folkstone Park, Wakefield and Accotink along the way.
In the end, my ride totaled about 58 miles and took me just shy of 6 hours.
Most of the advice is the obvious stuff.
1. Be fit enough for the mileage, even though it's mostly flat
2. Have a bike that's in good condition
3. Bring tubes, tools, etc and know how to use them
4. Bring plenty of water, especially if you hit a hot, humid day.
5. Bring plenty of food--you'll need it.
(caveat--you'll be in an urban area most of the time, so if you need to grab a bite, you're never far from a convenience store--just know where they are.).
6. Weather can be an issue--don't go if it's raining or has rained a lot recently--the Difficult Run becomes an unrideable mud bog very easily.
There's just two word of additional caution.
1. When you join the W&OD, be looking very carefully for the reentrance to the CCT--when I rode, it was not signed and was inconspicuous to boot. I rode right by it and foolishly ended up doing a few extra miles on paved path. It's really pretty soon after you join the W&OD--keep your eyes peeled.
2. Familiarize yourself with the map,know how to read it and be sure to bring it with you. Being an urban area, the trail is frequently interrupted and often relies of pieces of street to join sections of trail. Things get particularly confusing in the residential areas toward the southern end of the ride.
Good on ya' for taking this on. Its as close to a legit adventure one can have in suburban NoVa! Enjoy and let us know how it went.