If you have in mind one of those 200 lb trailer kits with a load capacity of around 700 lbs that can carry 4’ x 8’ sheets of plywood when assembled, any car can pull it. The load, however, will vary to stay safe dependent on the size of the car. I have pulled one of these loaded to around 700 lbs total including the trailer for thousands of miles with front drive compact cars with no problem.
We have also pulled a lightweight (450 lb?) folding camper trailer with a rear drive car so we have seen it both ways, with rear and front drive. Either rear or front drive worked fine for us.
If you are talking about a 1000 lb. camper trailer then a larger car, I suggest medium size, and a trailer with trailer brakes will be good.
Again, front drivers make a good trailer puller. We used to go camping with people who pulled an Airstream trailer with an early front driver, an Oldsmobile Toronado. They had no problem either.