Yes, the training center can issue the COMM or ATP along with the type. You'll have to:
1. Pass the FAA knowledge test (the written exam.) and
2. Have a current FAA medical certificate
before your checkride and
3. Have our TSA approve your training.
before you you start the sim part of your training.
As to what it'll cost, as fernytickles said, search the web, not pprune. Flight Safety and Simuflite are the two big business jet training companies in the US, they can answer all your questions.