How long is this adventure going to be?
Personally, I like traveling solo on road trips. I did my first cross country drive-a-thon when I was just out of high school. To go to all of those places, I hope you have several weeks set aside. In round numbers you are talking close to 20,000 miles with the likely side trips and the return run to Florida. That requires a lot of gas money!
All of the places you mentioned are worth seeing! Camping in national parks in July/August can be tough without reservations.