Any training class is only as good as the trainer. You can find a good one in PetsMart or a bad one at a so called training club. You need to feel comfortable with the trainer and the methods being used. If your not then look for another one.

About the puppy shots, after the third set (usually around 12 weeks) I would wait about one week and then enroll in class. This gives the pup enough immunity to be protected. Consult with your vet though for their recommendations.