Unlike the US or Canada Mexico does not receive many immigrants. Any one who is not born in Mexico is considered a foreigner. All foreigners have the same civil rights as any citizen of Mexico.
If you decided to go to Mexico you can get one of three types of Mexican visas. The first is the tourist visa. If you want to stay in Mexico permanently there are two visas available.
The FM3 is meant for people who do not qualify to stay in the country forever. The visa is for people who will be a 'visitor non immigrant'.
This is for people working in Mexico or going to school in Mexico. The last category is for people who are eligible to stay and live in Mexico forever. It is much like the Permanent resident card in the US.
You may need a Mexican Immigration lawyer if you decide to go to Mexico for an extended period of time. They can help you with any visa situation that may come up.