Welcome to the RTA Forum!

The basic idea you've laid out is the single most popular outline on this forum, so the first thing I'd recommend is simply spending a little time looking around which will provide all sorts of good information for you about what to see, stay, do, and for how long. These are a good starting point of some of the many great threads here.

For time of year, there are positives and negatives to any time, but I'd consider Sept./Oct. when you're past peak tourist season, but before winter. Remember, mountain passes like Tioga in Yosemite National Park are typically closed into June.