Ah, if only October were about six times longer!
Yeah, that time limit affords only a few days in each location. I see this trip as more of a "sampler" -- a preview of future trips.
The budget, assuming a six-month length, is around $30,000. That assumes 25,000 miles driven, about half the nights spent at friends' homes (I'm 28, so couch surfing is still cool), about a month of camping/backpacking, and the remainder at relatively inexpensive (<$100/night) rural motels. Plus food. Plus a big chunk for "???". (The actual budget has more detail, but this gives a general picture.)