Sounds like a good idea to first drive the route (after mapping) and check road conditions and shoulders (I drive every ride I make first...just cautious I guess). Now, I haven't done any cyclo-camping in years (I did those types of things in JR. High and HS...then found drugs girls and beer) but three or four day self-supported trips are fun if you have the right gear, a good deal of know-how in fixing your rig, and a lot of time. Panniers and the like would cost hundreds of dollars, and some stout tires and wheels (pretty sure touring wheels still have a lot more spokes and are thicker ie.28c) would only add to the dilemna- a better option, especially for the first time out, is to go credit card touring, and arrange to stay in hotels, motels or hostels (if you are young enough)...or campgrounds near restaurants or stores, we even stayed in old Presidion bunkers in San Fran once- that was a kick. These are just some suggestions top make the ride more fun.
Now the real strong suggestion, do not do a trip of that magnitude alone...always take a friend along.
I will do one again someday, when my wife is up too it (got her first rig at 30)- they are calling to me from my quickly dissapearing youth
Cheers, and good luck in your endeavor