Used road bike, even ones people shit on can be worthwhile. Have a friend or your LBS inspect/tune it up.
Some way to carry food and water
Tools and parts for fixing problems beyond just a spare tube - ie spoke wrench and spare spoke, baggy of 2-4 spare bolts (or nuts/bolts if your bike is that old), some mini pliers to pull thru a cable that comes loose and rips the endcap off, etc.
Plan your route, if possible, with knowledge of every bike shop and department store along the way in the event of emergency.
Churches and libraries are good for water fountains for a bottle refill.
Use a burner (30-60$) smartphone with OSMAND for GPS - it works without data and if your bike falls over while your regular phone is mounted you won't risk smashing it
Watch bike fit videos if you will be that long in the saddle
Get a cheap noseless saddle to not destroy your dick
Read and understand all local laws for bikes (both state and including town ordinances where you'll travel) to not run afoul of them.
Sun screen, sun glasses or goggles
Lights, reflectors, bell
Ride with traffic, don't run lights, don't be an asshole.