There are small camper vans for rent. That will give you a sink, fridge, toilet and a bed. It is a compromise between a small motorhome and a basic van.
But if you have a tight budget just go for a basic van and then do the 5 gallon bucket and camping pads for a bed setup. I did 3 week long camping trip in France in a small rental car. I managed with a tent, sleeping bag, self inflating camping pads and a small inverter that plugs into the car 12v socket. It does not require much gear to have fun. I did not have a stove and I did not even get an ice chest . But I did get a knife fork and spoon at the grocery store and paper plates, bowls, cups and some trash bags. Having gone car camping for more than 30 years at that point in time I knew how to be minimal but comfortable.