Oh, that makes sense. Pecos is a sparsely settled area of Texas. Geographically, those parts of Texas are classified as "frontier" due to the terrain and low population densities. The population is primarily Hispanic and the economy is rural - ranching and farming. That area of the state is desert-like, and towns are very far apart. Summers are intensely hot and winters are very cold. It has a lot of historical significance associated with the early days of the cattle industry and these days it is primarily known for producing cantaloupes. It's not really a tourist destination - rather, a stop-over on the way to Big Bend or on the road to California.
Have you actually visited Pecos? If not, I would encourage you to do so prior to making any sort of commitment. There is a good reason that they are willing to deal with immigration sponsorship. . . I certainly don't want to come across as negative, but the area may be too much of a drastic change for you.
I would venture to say that there is very little public transportation in Pecos. You will need a car with very good air conditioning - LOL. There is an airport, but I don't believe that they have any commercial carriers. So the closest airport is Midland-Odessa, I believe - and that is pretty small, so you have to catch connector flights from a larger hub. There are not a lot of housing choices or availability. As I recall, there are many large mobile home (caravan) parks which serve as an alternative to traditional housing for residents. I'm suppose that recreation/leisure activities are the same as most small towns in West Texas - rodeo (in season), dances, and driving to the big city for a night on the town... which would be Midland-Odessa in this instance.