The visa is something you will have to find out about.
As others have said, part 141 has lower flight time requirements but you also need to factor in the required ground instruction as part of your expenses. Find out what they will charge you for ground instruction.
Another thing thing to look at is the price difference between 141 and 61 schools as far as rental costs go. Some of the bigger part 141 schools charge more for the planes than the smaller FBO type 61 schools.
Some smaller part 61 schools may not have a twin for you to rent for ME/MEI.
I have instructed at both types.
Good luck.