The term type rating is only used in FAA land to denote an aircraft which is over 12,500lbs, a turbojet regardless of size or weight and anything the "Administrator" (FAA) has deemed so complex or dangerous to the uninitiated that it requires a type rating.
"Type rating" as in make & model doesn't exist in FAA land.
'Check ride' is FAA nomenclature for a flight test with an examiner.
It's not a check flight were a box is ticked by an instructor.
- written test
- Training as required to get an instructor sign off for the flight test
- practical test with examiner.
Since you're training for the issuance of a certificate or rating you will need an M1 visa also.
You will need to find a school which is certified by the FAA under Part 141 as they are the only ones that can issue the I20 visa application form.
Unless you're like a Green Card holder or dual citizen obviously.