I'm not really qualified to answer this since, while I am a Mexican Permanent Resident, Mexico dramatically changed its immigration system in 2012 and I was grandfathered into that status as part of the transition from the old system. I thought you should get an answer, however, since you do need to apply for visas to live in Mexico long term and you may need to do this before you leave your home country.
While I've not found an official source, an unofficial overview of Mexico immigration is available here. You need to apply for a Temporary Resident visa if you are planning to stay for more than 6 months. Under the old system you were able to enter Mexico as a tourist and change your status once you got there but under the new system at least some of you must apply for this from outside Mexico (I think the close family members of a Temporary Resident are able to apply inside Mexico later if there's a reason to do this). I don't know if "outside Mexico" can be anywhere or must be be your country of residence, so you really need to figure this out before you leave home.
Note that Mexico doesn't have different visa types for different purposes; instead the activities you are allowed to do while in Mexico get attached to your Temporary Resident visa. The "normal" applications would be for employment purposes, which you would document with a letter of offer from a Mexican employer registered with the IMN to allow them to hire foreigners and which would allow you to do that job, or as a "rentista" (a person of independent means, e.g. a retiree with income from outside the country), which you would document by showing bank statements with a sufficiently high balance or sufficiently large income and which would allow you to live in the country without working there. Your own purpose is clearly neither of these, and is complicated because the (Mexican) organization you'll ultimately be doing volunteer work for doesn't exist yet, so I'm pretty sure you are well into territory where you'll need a local lawyer to help with both to establish the organization and to do the paper work to get permission to conduct your work with the organization attached to your Temporary Resident visa. My situation was vaguely similar to this (I became a board member of a Mexican charitable foundation and needed to become a temporary resident with permission to do that "work" despite it being unpaid) and I couldn't have arranged this without a lawyer to produce the papers I needed. Since getting this done yourself is likely impossible outside of Mexico, and if your sponsor isn't doing some of the ground work for you, you may need to apply as a rentista and hope they won't mind what you are doing while you work with a lawyer to establish your ultimate status and get yourself ok'd for that. Or something.
The initial Temporary Resident visa will be for 1 year. What you'll get before entry to Mexico is a stamp in your passport indicating the consulate approved your application; you'll need to visit the IMN office where you live once you enter to complete the application and obtain the Temporary Resident card, which you'll need for things like opening a bank account or getting a driver's license. After the year you can apply to extend it to 1, 2 or 3 years more. Once you've spent 4 years in Mexico as a Temporary Resident you'll need to apply to be a Permanent Resident instead. If you think you'll stay that long, be aware that becoming a Permanent Resident will change some of the conditions of your stay. The particular issue some people have is that while a Temporary Resident can possess and drive a foreign vehicle in Mexico (and it is generally cheaper to buy a vehicle in the US) a Permanent Resident cannot.
Good luck! While Mexico can sometimes be excessively bureaucratic I've always found the immigration people to be friendly and helpful so there's no reason to fear any of this. Also, don't treat anything I've said as authoritative other than the fact that you need visas to live securely in Mexico and you need to organize that before you go. The Mexican embassy where you live may provide better help if you can find someone to explain your situation to.
