Four weeks is a generous trip
A four week road trip will enable you to see a lot of the country. Even with 4 weeks, you can't see everything. I have been roadtripping in a serious way for over a decade (several hundred thousand miles) and I have only seen about 20% of what there is too discover in America.
Prices of rental cars -- there is plenty of tips on this board for ways to get good rates (use the search function) but the companies provide no-obligation prices on their sites -- use them.
Again, use the search button (gray) and search for budget tips -- there are hundreds of suggestions here.
What kinds of things interest you?