I'll also give you a little encouragement and advice. I had a friend who when he graduated from college decided to ride his bike across the country over the summer with little more experience than you apparently have and he made it. He started out doing 30-40 mile days and rode himself into shape and by the end of the trip he was doing 4-500 mile weeks. You all are young and if you're not playing video games all day and you start taking your prep seriously NOW, you should be okay.
I think your inclination to go with a used road bike is a good way to go for the amount of money you want to spend. Reading this is probably a good place to start:
Alternatively, you can also buy a used cyclo-cross bike and that can work very well for touring. I was recently looking into buying a used 'cross bike and there were several pretty nice ones for around $800.
Whatever you buy you need to get it sooner rather than later and start getting out on the road. More than any issue with getting your legs ready, you need to get used to dealing with traffic and you need to get your backside prepped for being perched on a bike seat all day, every day.
I think it would also help you to find a local expearienced cyclist who is willing to go for a 1/2 dozen rides with you and explain the do's and dont's of being on a bike and out on the road.
Also take note of the of the "How to Department" on the ACA web site for lots of information you will find useful for what to pack.