Are you thinking of the Rails-To-Trails route? http://www.atatrail.org/
If so, yes, it is fairly flat with long, slight grades as it is an old C&O Canal and RR right of way. It's mainly packed, crushed stone and dirt...and unimproved and rough in some areas.
If you are wanting to ride this trail, you will need a mountain bike or road bike with wider, durable tires and wheels. A flat bar bike would be desirable, I would think. At 335-350 miles in length and given your 8-day schedule, 50 or so miles a day should be a fun and challenging range on the somewhat slower trail surface and getting you through the rougher, unimproved areas without having to push too hard or spend 10 hours in the saddle.
The Rails-To-Trails organization takes an annual group ride across this trail: http://www.railstotrails.org/index.html
I have talked to a couple that rode the entire trail and they said is was a nice ride.
If you don't own a bike now, go to a bike shop and explain your goal and describe the surfaces and terrain you will be traversing. Print some pictures of the trail and of the riders and their bikes that are pictured on the trail and show them what you want to do. Any good shop will sell you a bike suitable for trail use and any equipment you may need to carry the gear you will need while on the trail. Then, get out and ride and get in shape prior to your trail ride.
ETA trail basic info link: http://www.atatrail.org/tmi/about.cfm#location
