I'm sure others will chime in here with better advice than I'm qualified to give. I would guess that some of these decisions are insurance issues. I have BCBS of Arizona, and they just give me a list of providers--I don't need referrals or anything, so if I want a 2nd opinion, I just go to another person on the list. Pretty painless, actually.
In my case, my cardiologist did all of the tests, including the heart cath. In fact, I didn't meet the surgeon until after my cath. My cardiologist wanted to verify everything with the cath before sending me to the surgeon. Again, on my insurance plan, I could have seen the surgeon sooner if I had wished.
My cardiologist is Myron Licht, also near Lincoln-Deer Valley Hospital. Again, heard a few good things about him and felt very comfortable with him after I met him. He works pretty closely with Dr. Pang (the surgeon), which I liked. Lincoln-Deer Valley is a smaller hospital (pre-renovation, at least!) and the doctors seems to know each other, which made me feel better for some reason.
Maybe more people will jump in with recommendations for Arizona. A second opinion is always a good idea, especially if you don't feel your first opinion got to the bottom of things.
Are you in the Phoenix area?
Tim