This is just a brief synopsis of the three types of visas. Real estate can be purchased by someone holding any one of these three visas.
The first type is the FMM commonly referred to as the tourist visa, or visitor's permit. The FMM is the form you will receive if you arrive by air, or can be filled out at any of the border crossings. The tourist visa is valid for a maximum of 180 days and cannot be extended. When it expires you need to leave the country for a minimum of 24 hours to return with a new tourist visa.
The cost of this visa is roughly $ 25 US Dollars and it's usually included in the price of your flight. If you arrive by car you'll have to pay this fee at the border.
A Temporary Resident Visa, visa residente temporal, is intended for those people who wish to live in Mexico for more than 180 days but no longer than 4 years. The Visa is first issued for 1 year and then can be renewed for a further one, two, or three year term. To get a temporary residency Visa you must apply at a Mexican consulate outside of Mexico. And you must meet financial requirements of income, investment, or real estate.
The financial requirements fluctuate a bit each year and do seem to vary from consulate to consulate. Once pre-approved at the consulate a Visa stamp will be placed in your passport. You then complete the process to obtain your green card within 30 days of your arrival in Mexico at the nearest immigration office.
The third type of Visa is the Permanent Resident Visa or visa residente permanente. This visa is intended for people seeking permanent residency status in Mexico. If you have a temporary residency Visa, you can apply from within Mexico to have your visa status changed to permanent.
Or you can apply in a Mexican consulate outside of Mexico without first applying for a temporary Visa. You must meet financial requirements and once you're pre-approved the process is completed at the immigration office within 30 days of your arrival in Mexico.