I look for an instructor who can provide student references/evaluations. I also look for one who details specifically what they intend to teach. If I want to learn to shoot well then I want a shooting class, not a gunfighting class. On the other hand if I want to learn to fight with a pistol then that would be another story. Then I want an instructor with proven credentials specific to that activity...not theory.
An instructor must be able to "teach" not just "present" material. Many people have the knowledge and technical ability required but are unable to teach effectively. A good instructor has to be able to put themselves in the student's shoes and figure out a way to impart the required knowledge to them as an individual. What works for some may not work for others and the instructor has to be able to adapt and bring that student up to speed.
Many ex-military instructors try to teach civilians with the same harsh, intimidating style they used with soldiers. I personally think this is a mistake and few people are willing to pay moderate to large amounts of money to be denegrated by an A type drill instructor.
Granted there are times when the instructor may have to exert control with a student who is getting out of hand but this is much easier to do if the rest of the class has been presented in a calm, even demeanor. This makes the rare instance of necessary "roughness" by the instructor stand out as something different that requires an immediate adjustment by the student.
Certifications, while helpful and nice to have, don't tell me much more about an instructor's ability to teach...only that they attended a class and passed it. I instruct. I don't teach gunfighting because I've never had to fight anything except targets in competition...challenging though they may be, they are just targets. I teach defensive shooting skills and had instructor certifications from several sources in the past. It became too cumbersome, for several reasons, to keep all the certifications current but I'm still the same instructor I was when I had them. I proudly provide references for prospective students and ask for evaluations after every class even though I don't teach for a fee any more and only teach friends, family and interested club members these days...age is starting to slow me down