Middlegate and Coldsprings Station have relatively inexpensive camping available, as does Bob Scott Summit (just to the east of Austin). I stayed in motels (except for Cold springs) but I was pretty whacked at the end of each day's ride. I was 61 years old at the time and I appreciated the comfort of motels. I also avoided getting snowed on in Austin by being in a motel.
Make sure you know which days the stores in some of the smaller towns are open when you are going through. For example, Baker in Nevada, has only a small grocery store, with limited supplies, and a restaurant which is closed on certain days.
The riding is not exceptionally difficult if you are fit, which you all appear to be, but it is definitely challenging, and you will be carrying panniers.
The country between San Francisco and Cedar City, is magnificent. Enjoy your ride.