Personally I think that AC maps are worth it if they go where you want to go, but you can do without if you prefer. I think that if anything they saved us money by allowing us to better plane where we could stay for free. They listed a bunch of places to stay that we may or may not have found otherwise.

Most stuff can be pretty inexpensive. Cooking isn't required, but a single pot and a home made pop can stove will get you by. Check out the Zen stoves website.

You can get by with a fairly inexpensive tent and sleeping bag. Something like the Slumberjack Superguide bag and one of the Eureka tents will suffice and can be quite inexpensive. I would buy a comfortable sleeping pad though even if it costs a bit more.

We managed to stay for free more than half the time and probably could have more than that with no need for stealth camping. Avoid the KOA type places if you can as they are expensive. Some states have great state parks and state forests with cheap camping. City/town parks are good options. Sometimes we stayed in churches which we usually only knew about because of the AC maps. In the middle of the country it is pretty easy to find free places to camp, but harder near the coasts.

A frugal person can probably make the trip with $1000 to cover daily expenses if they watch their pennies. It would be a no frill way of going but could still be quite pleasant. On $1500 you would be able to relax with spending a bit more, but still need to watch your pennies. On $2000 you could just spend on what you felt like, even getting a motel room or splurging on other stuff once in a while, at least if you are a cheapskate like me.

I figure that once I have the gear and plane tickets out of the way I spend close to the same when I am on tour as I do at home. I have to eat where ever I am and I am not putting gas in a car when on tour.