Hey Sarah, i did just that in June, had never done a road trip before and had lotsa questions, overall my attitude is one of "Just do it" as far as a bike goes i would go to the local bike shop and buy new or if they sell used ones there that would be okay too, their is something to be said for the service and tune ups and all.
We used Trek mountain bikes, of course we were pulling a 60 pound trailer loaded
with gear. We did change the tires however.
As far as the mapping some states have road maps just for cycling, TN was great, i would contact each state you will pass thru and see if they have anything, also
adventurecycling.com has maps for certain routes, i bought a few but decided to wing it. Pedaling.com is also a source for routes, hope that helped
remember...."Just do it"!