With that in mind...
Lots of folks have recorded their TA experiences in journals. Tons of them are on the Crazy Guy on a Bike site. You can start with ours at:
Cost is WIDELY variable. If you camp and cook most of the time you can go pretty cheaply.
We averaged under $5 per night for campsites and motel rooms, but we very seldom got a room and stayed in city parks, churches, and other free places whenever possible. The AC maps were a great help in finding these places, but we also seeked out others on our own. We got some invites from generous hosts, which also helped a lot.
I don't have an exact accounting, but spent around $2k including airfare (one way only since we were picked up by family at the end)and everything I spent during the trip. This included shopping stops at the Patagonia outlet and the Pearl Izumi outlet. It also included quite a few restaurant meals and things like a rafting trip on the Salmon river.
I actually think I would have spent more if I were at home.
While we were on the frugal side, a true cheapskate could get by cheaper and some who want to stay in motels and eat in more expensive places will spent several times that much.