Hola Mayan,
Based on your Mexican license, the FAA will grant you a PVT certificate and if you take the "Instrument Foreign Pilot" written test you will have an Instrument rating on the PVT certificate. And they will put the B-737 rating on it but again, only at the PVT level. That doesn't do you much good looking for a job. Normally you must hold a FAA PVT before you get a FAA COMM and a FAA COMM before you get an FAA ATP. Holding a foreign COMM or ATP does allow you to skip the FAA PVT and COMM and go straight to the ATP. In addition, as the holder of a foreign ATP, you are not required to have an instructor's sign off to take the checkride. So you still need a FAA medical, you'll need to take the ATP knowledge test (written) and pass a checkride. If you take the check in an Aztec (I had to use that example), you will get an ATP MEL. If you take the check in a 737 sim, you will get an ATP MEL B-737.
In the US, there is only one 737 rating that covers the 100 to 900. There are several training centers that do 737 training (I do work for one on the side but not in the 737 program.) I think they all do the basic rating in a 200 and then add on a NG differences program for those who want it. The basic rating cost around 7-8000 dollars. You should not need a full course being current on the airplane. I think you'd fall under "Upgrade" training, 4 or 5 classroom days and 3 or 4 sims v. 2 weeks and 6 sims. So it should be a bit cheaper. Or just do it in an Aztec, that should not be over 2000 dollars.