Don't be afraid to shop around for an Instructor, when you start diving you're usually put in a group of other beginners and you learn the basics from the Instructor you're given. When you advance to Tech diving you will have a pretty good idea of what kind of Instructor you learn best from so try and assess your potential instructors before you invest in a course.
A great way of trying out new Instructors is TekCamp; over five days Instructors from all around the world and different training agencies all come together to teach groups about their chosen field which is a great way to get a taster of the different courses and training styles available. Also at TekCamp you will find many of the equipment manufacturers with their newest equipment for you to look at and this is the perfect time to talk to the manufacturer and Instructors to discuss the efficacy of a future piece of kit. it's a great time to socialise with Instructors, get their opinions and try out new pieces of kit.
Do they often dive just for them, just for fun? Many Instructors only dive when they teach so they are repeating the same dive over and over just with different students. Skills and procedures come from real world procedures so you need to find someone who gets out there and uses the skills that they teach in the real world.
As an Instructor; when you teach a course often you get into a routine and you adapt it to how it works best, if you don't teach a certain course very often you can get a bit rusty and maybe miss parts out or use out of date procedures. Instructors who have taught in a wide variety of environments have stories and experience that will help make their courses better and more natural and more fluid.
Not something you really want to know but when you think about it: do you really want to take a course that you can't fail? The Instructor is either very good at what they do or the course isn't very demanding. Experienced Instructors will have reached a level where they can say no to a student until they are happy that they will be alright by themselves without the Instructor present.
It's quite easy to climb the certification ladder by just taking courses without having any relevant experience; I once knew of a PADI Course Director who had never been diving in the Ocean or Sea, only inland lakes. This type of Instructor will probably be great at the core skills but will be less flexible when things don't go exactly to plan.
With many things in life; you get what you pay for. If they are a full time Instructor who dives in their free time then their sole income will be their fees they charge. If the course works out quite cheap you need to ask yourself why and if they're cutting any corners to reduce costs. It might sound harsh but at this level if you go cheap you may not get a chance to try again with a different Instructor.