Category 3 is for pilots training in any aircraft with a MTOW of 12,500 lbs. or less. (Note: in many cases Category 3 is waived and no TSA application is required. Check with your learning center).
That is a little misleading. There are strict criteria that determine what might be exempt. Essentially, first issue of a full FAA certificate (whether it be Private or Commercial) requires TSA - even for somebody who may already hold a 61.75 based on cert.
Check out the FAQ on the AFSP website:
https://www.flightschoolcandidates.gov/afsp2/?acct_type=c§ion=WN#faq
in particular step 2.
as is Step 8 in the category guide as who must apply:
https://www.flightschoolcandidates.gov/afsp2/?acct_type=c§ion=WN#guide
Originally Posted by Chinchilla.612
As I say though, best bet is check what your training provider wants you to have and go with that.
A lot depends on the training provider's own status with SEVIS.
If they are not SEVIS approved - you may find an unscrupulous flight school possibly tell a student that s/he doesn't need a M1 Visa (for example) - because they are not in a position to sponsor the student - rather than turn business away.