What preparations should I have to fly from the US to Mexico?
AOPA has a guide here. I think it should cover most of your points apart from visa/immigration, because that isn't really an aviation issue (unless perhaps you're commercial air crew using a flight crew visa). Don't forget to plan ahead for re-entering the US, there are a bunch of requirements for that too, including using eAPIS.

Some points from the guide are:


Documentation: you need a radio license for the pilot and the aircraft
Insurance: add Mexico to your insurance policy if it isn't already covered
Flight plan: you must be on an IFR or defense VFR flight plan to cross the ADIZ
Night VFR isn't allowed in Mexico (with a few exceptions for flights to the US)
It looks like the more paperwork you have with you, the better
FBO services are likely to be more limited than in the US, and fees are often higher


Also check out the Caribbean Sky Tours Pilots Association, they publish a pilots' guide to Mexico and Central America.