I have over 50 yrs of camping experience in USA, Canada, and Europe. I now live in New Mexico, but travel a lot in the southwest.
Camping in this part of the country can be very cheap. In NM, many campsites with water only are $15. More if you want electric. But there are good bathroom facilities included. In other states in the SW, there are lots of places where camping can be free....in the desert. It is best to have some kind of camper, however...up off the ground.
Throughout the '60's and early '70's I pulled a 1200 lb popup with a VW bug...only 1200 cc's. We went all over......to Maine, SE states, and all of eastern Canada. We only needed a bigger car once we headed west and tried camping in the Rockies.
When pulling a trailer with any car....be careful. If you exceed the weight limit that your car has specs for.......your insurance company will pull the plug if you have an accident.