The problem we found with owning our own place (4 acres W/well/septic/electric/buildings 2 mi down stream from I-25 on the Pecos River) is that you have to go back there 4 times every year, at a minimum. We need to check the place after the thaw in Spring, during the "monsoon" in summer, winterize in fall and once in winter see if any "critters" have tried to move in. Having a permanent place gives you somewhere to go back to but it also requires maintenance, security, and checking up on.
To answer your question about prices. Del Rio, Tx has Holiday Trav-L-Park near Lake Amistad with monthly rates of around $300 (last I checked) plus electric. They do have a club house, boat storage, and some activities. It is to hot in summer to stay there IMO but for 9 months of the year it is not bad-windy at times-but not bad weather most of the year. Great fishing/hunting spot if you like to fish, hunt, explore.
Another option is you can stay in NM State parks for 14 days for $4/day at W/E sites if you buy the $225 annual use pass. Most state parks are close to other state parks so you can go from park to park within a small area and stay 14 days at a time in each. one.