It is hard to estimate what you will spend. We vary widely rider to rider. Heck I vary widely tour to tour.
That said I have found that a free place to camp can be found the majority of the time, especially in the middle of the country. City/town parks church yards etc. Just ask around. If it is obvious how to find the local police I might start there. I don't always expect permission and might ask a store clerk "Do you think anyone would bother me if i pitched a tent across the street in the park". If that fails I might ask about other possibilities. Librarians tend to be very helpful in small towns and may call around and find someone who will let you camp. Churches are another option.
On the west coast the hiker/biker sites in Oregon and California are nice, cheap, and available.
As far as daily expenses, I am pretty comfortable on something like $20 a day, but could fairly easily spend as little as $10 per day or as much as $30 a day depending on the trip. Personally I try to have a lot more than I will need available and spend what I feel like at the time. I like to budget time similarly if possible. It is nice to not have to feel limited.
I think buying the AC maps for the first leg of the trip is a good idea for two reasons. If you are unsure of how to find places to stay they will get you started and then it becomes easier to know where and how to ask. Also you can evaluate whether they are worth it to you. Then if necessary you can have more maps sent via general delivery.
Personally I find the maps worth the cost if I am going somewhere they have maps for.