Long story short: The OP has an unsuitable bike.
I'd agree that there are better bikes for this purpose available, but "unsuitable" is a bit strong. This probably isn't any worse than the hundreds of original Bikecentennial bikes with galvanized wire spokes and thread-on freewheels.
Back to the original question: first you need a way to carry a load -- if you're going to ride this Trek, you'll want a trailer. For racks and panniers to work, you'd need stronger wheels (with more spokes) and a stronger frame.
Second thing to get is a tire pump, spare tubes, repair kit, and probably tire irons. Frame, miniature, floor, doesn't matter; you're going to have flats. My daughter and I made it across the country without breaking a spoke, but we had enough flats to make up for it.
You'll want to decide fairly soon if you can afford (and want) to do this trip inn-to-inn (really motel-to-motel), or camp. The second option involves camping gear (tent, sleeping bag and pad) and cooking gear.
You can push the bike (+ trailer) up hills if you're geared too high, but you'll get to ride more if you get lower gears. That's going to require either a really compact double (mountain gearing, about 24-36), or a triple. If you go with a triple, and your bike shop has to change shifters and derailers, you're half way to the to the cost of a "true" touring bike.
Look at the Howto section off the magazine page on this site, or check out some of the ride blogs available. Mine is backward, as I wrote up an "Unpacking" page to document what made it across the country, instead of list everything I packed. And that was still too much...