Originally Posted by Flyhayes

This is incorrect. A tourist, on a tourist visa can undertake a course of study as part of their vacation. There is a limit to how many hours you can spend learning per week without a student visa (something around 15hrs/week iirc).

You will need to complete the TSA screening regardless of visa status, this can take several months to complete the first time.

If you need a student visa to undertake a prolonged course of study, part 141 schools are the only ones that can be authorized to give them (although not all have sought that authorization).

If you can start training at a part 61 school, you're likely to spend less money. However, since a tourist visa typically won;t allow you to stay for a great length of time, you might need a part 141 school to finish your other ratings at.