I rode from Pittsburgh to Washington DC during Hurricane Irene. I had no problems using 26x1.5, 38mm, Continental City Contacts, despite the heavy rain on the C&O due to the hurricane. Don't overthink it. If you can go up to 38s I would, or just go up to 35s.

If you don't have fenders, I would suggest it. Just make sure you have decent clearance between the tires and fenders. I ride the GAP often and got tired of cleaning the drivetrain on my wife's fenders bike. The drivetrain gets a lot of the crushed limestone on it. She now has fenders. On the C&O on a rainy, muddy day, you'll be happy you have them.