Change the oil, check the other fluids, plugs, belts, hoses and brakes. Make sure your spare has air, and you have all the jacking stuff.
Pick up an extra set of belts and any tools you'll need to change them. Familiarize yourself with how they're routed and how to install.
Make sure you have your cell phone, and honestly a cb radio is a great idea too. You WILL be driving through dead zones, and ch 9 is an emergency frequency. ch 19 is the standard open channel of choice and you can find directions and cops just by asking / listening.
An extra set of plugs and a gas can couldn't hurt if you have room.
Bring a gallon of water, and flashlight too.
FWIW, I spent 3 months travelling the states in my Mustang (covered 26,000 miles) with the above supply list. I never got lost or stranded, and wouldn't think twice about doing it again.
Most of all, have fun!
2002 BMW 530i
1997 Ford Mustang GT
1995 Honda VFR 750 (For Sale)
1964.5 Ford Mustang