One set of maps will do nicely. If you don't have one yet, a map holder, handlebar bag with map holder, or front rack and pack (with map holder) will help greatly.
I'd recommend a cyclocomputer just for the odometer. (Get one to display daily mileage and cadence if you want -- cadence is sufficiently meaningless that it won't distract you, and may even help on some of long climbs.) Out west, you may not need it; only cross road in 15 miles, or 60 miles, is usually distinctive enough that you don't need much help. In the east, particularly in the mountains of Kentucky, Missouri, and Virginia, the odometer really helps. Next turn after 3.2 miles can be anywhere from 7 minutes to 30 minutes, depending on slope and how tired you are; and you might have passed a dozen other roads in the meantime.
I think my favorite was somewhere in Missouri, where they had the number of a metal ID tag on a telephone pole to identify the turn. Even though I couldn't find the number when I inspected the pole, I got that one; the one in Kentucky with no road sign, I missed. Fortunately the family on their porch a quarter mile up the road set me straight!