Get some good maps to see just how much there is to see and enjoy in half the US.
More than 9000 miles in little more than 4 weeks works out at more than 2000 miles per week, that is 4 days of doing nothing other than driving each week. Only you can decide if that will be 'enjoyable' and 'fun'.
Might I suggest that you cut that down and concentrate on the eastern half of the US. The historical, natural and other attractions in this part of the country can make a great trip, and you would actually have time to see and enjoy all the places you visit.
Dave mentioned a good sized wall map. that is a great idea, but for more detail of the routes and attractions, it would well pay you to get hold of a Rand McNally road atlas. If this is not available locally, you can purchase one from the RTA store via the link at the bottom of this page. If you order it now, you will have it in a couple of weeks. It will show you all the roads and routes available to any attraction, and most, if not all the attractions along the way. You will see so much more detail than you will on a computer screen.
Whatever you do, do not take travel times from computer programs. They are unrealistic and do not relate to real time on the road. As a rough rule, assume that every hour you will be covering about 50 - 55 miles - including all essential stops, but not sightseeing.
On a budget, what accommodation are you thinking of using - Motels or camping?
Lifey