Hi Jim,
There are lots of people riding hybrids on the GAP and C&O. There are also plenty of bicycle shops along the way, just in case you have a mechanical issue. The most important thing for you to find in a bike is comfort, something that will be comfortable for hours of riding each day. No one can really tell you what works for you, as a lot of it is trial and error.
You may even want to consider just renting a bike from Golden Triangle in Pittsburgh or C&O Bicycle shop in Hancock, MD.
I could recommend plenty of bikes, but what matters is what is available to you at the local shops. What do they carry? What is your budget (for both bike, and for gear)? Do you plan to camp along the way or find a bed at the end of each day?