I'm thinking about trying to buy some property in either New mexico or Montana as a vacation/hunting place. Has anyone ever done this?

I'm from Florida& would really like to buy a small place thatI could go to each year with the family & get to know the place, town, people, etc. I figure I can get the most bang for the buck in the above two states, but would be interested in what others have to say. My ideal place would be a small cabin on several acres that was next to public land. I'm not rich so buying some huge ranch is not going to happen. Anything I'm missing or need to look out for? Anyone know anyone that could assist me in the search?

Thanks for the help!