I can't give you any references to good trainers in NJ but you might check with shelters and your vet to see if they recommend anyone.
Questions you can ask a prospective trainer would be:
What training method do they use? - make sure they use positive training methods, not forceful/jerking the dog around methods.
That is the main one I can think of, the other thing you should do before you sign up is sit in on a class. That way you will be able to see how the trainer interacts with the dogs and what methods they use and If you like the trainer or not(very important).
I hope this helps. Good luck finding a class