SUV with Fridge rental
You are aware that the 'states' are hot or humid or both in July, right? Do you have any preferance for which state(s)? The higher the elevation, generally the more pleasant it is in the summer time. I recall that Colorado and Northern (Flagstaff/White Mountain area) Arizona weren't too bad.
Are you talking about tent camping? If so, a car rental agency may be your best bet. For motorhome camping, there are companies which rent RVs; some RV dealers rent out used units. How long a trip are you planning?
If you are primarily interested in going places, and the camping is a secondary interest, then a Class B (van camper) may be your best choice.