You all give such good information! I sure have plenty to keep me occupied for awhile!
I guess I am leaning towards a road bike, I like the idea of traveling far, being able to get up hills without a problem and the different spots to place my hands, something I didn't even think of until yesterday.
The cross country trip is just a jot on the sketchbook for now. SIL will in all likelihood be running not riding, so that I can spend my days either taking my time and staying close by him, or racing ahead of him and relaxing!
But, I realized that I am getting this bike for me, and no one else. Aside from that trip, whenever it happens, I will be riding for pleasure and fitness. I will be riding roads around my general area, which are paved and pretty much hilly no matter which direction I go.
I have a good place to start now, and will keep researching and be ready to start trying out bikes soon.
Thanks again everyone!