Agree with others--a sedan in the Toyota Corolla class would be fine. A somewhat larger car or a small SUV (Toyota RAV4 or similar) will give you more space. Your itinerary is a bit generic and misses some worthwhile places.
I guess I'm seeing a revised itineary--no Florida or Texas but places you could drop or reroute. Unless you like old house architecture al lot, I'd skip Savannah as its rather similar to Charleston but without the great restaurants, ocean access, etc. Going across southern Georgia and Alabama will be boring. Okefeneokee swamp and the barrier islands like Cumberland would be better uses of time. Chicago to the Smokies is a boring drive and frankly you'd be better off seeing less visited areas of the Appalachians in West Virginia in conjunction with DC. San Diego is nice but skippable. The traffic between there and LA is always heavy and the major routes are boring. You can hear the blues in Chicago--you don't need Memphis unless you really want the kitsch of Elvis' house.
Like others, I think you need objectives rather than a bucket list. National parks are not always the most notable places and many past their prime places are heavily marketed toward foreign tourists--so places that turn up on top 10 lists of whetever often aren't worth the effort.
August is heavy tourism time. Doing the bulk of your trip in Sept/Oct will get you the best weather and relatively few people at major attractions away from big cities. November means shorter days, with daylight ending before 1800 in many places.
