The tests that any good surgeon will require are:
manometry (tests swallowing coordination and strength, and strength of LES)
24hr PH monitor
As Joy said, finding the best possible surgeon is critical to the success of the surgery. (As a surgeon recently told me, it's also critical to have the right patient--that's determined by the above tests.)
When I had my surgery done, I depended upon the recommendation of my GI doc. I also double checked with friends in the medical field, and they concurred.
I am now in a new city, and have found here that there is one surgeon who "does all the Nissens". That would be the person I'd want to do mine.
I've heard a rule of thumb that the surgeon that you choose should have done at least 300+ Nissens. (The one in my city now has done 1000+)
Your best bet would be to call around to different GI offices and ask who they recommend. See if one name rises to the top.
This isn't a surgery to be taken lightly. You need to really need it--to be in a situation that is you can't continue to live with. It's not that the surgery is that bad...it's actually much easier to recover from that I ever imagined. It's just that you will have changes made to your GI tract that you'll have to accept.
You may not be able to burp or vomit (I can do both--vomiting isn't recommended, so those of us who've had this surgery always carry anti nausea drugs, just in case). If you have an overly tight wrap you'll have some trouble with bloating and gas--especially in the beginning. Sometimes certain things don't want to go through your wrap (For example, I have trouble with some pills. If I eat a lot of salad or raw veggies, my wrap gets irritated.)
You have to feel that the possibility of those inconveniences is worth it to you. I knew when I had the surgery that I would not be made "whole" again--I wouldn't have the GI tract I had as a teenager. I had realistic expectations, and do not sweat the little inconveniences. I had uncontrolled asthma caused by my reflux, and it was not a healthy situation. I am very glad I had the surgery and would have a redo without hesitation, should it be necessary.
This forum gave me the courage to go forward with the surgery. As you've seen, there are many posts on the internet that are frightening. I'm quite sure that those are people who did not have surgeons with sufficient experience doing their procedure.
People here were realistic and positive. Is it a perfect answer? Unfortunately, no. Is it the best answer? For most of us here, yes.
Good luck making your decision.