"What do I need to do to convert my Mexican PPL to a US FAA PPL?"
Contact the FAA - probably the Certification branch in Oklahoma City but you could also ask any regional Flight Standards District Office (FSDO).
"Part 61 or 141?"
The same information as given above also applies to you with selecting a school. If you select a part 141 school, however, you will need to complete an approval process through the Transportation Security Agency for permission to get flight training in the U.S.
"Student visa or tourist visa?"
I'm not an expert on this topic; maybe others can shed more light.