Welcome to the RTA Forum!
You've got a nice outline of great places to see, and with 3 months available for your trip that's a great amount of time to really dig into some of these areas.
My only concerns would center around this being your first time trip. This is a very major undertaking for a first time trip and that does bring up the thoughts of how much you'll really like spending that much time away from home. The other big factor is the budget - a trip like this will take quite a large amount of money, so I'm curious how much you think you'll have saved away for funds.