First off I want to clarify that I think that a proper cave diver training program is the most rigorous non-military/non-commercial dive training you will ever go through. That is because the cave environment is the most demanding environment that non-military/non-commercial divers will dive in. I can state this with certainty because I have been a military diving officer and a commercial diver, and have dived many places in my 45+ years as a scuba instructor.
Because the environment is so demanding, you should choose a cave instructor who also demands that you meet, or exceed the standards set down by the agency s/he teaches for. Ask for references.
It is important for you to interview the instructors you are considering for your cave training. Have yourself a list of questions that are important to you, write down the answers and compare notes of the instructors after you have completed your interviews.
At the same time the instructor is getting a better idea of who you are, your motivations, mindset and whether or not s/he wants to accept you as a cave student.
Some of the questions I suggest you ask are.
1. How long has the instructor
been an instructor? How many cave classes has s/he taught.
2. Ask about the experience of the instructor: is the instructor qualified to teach other advanced dive programs such as, deco procedures, advanced nitrox, trimix? Does the instructor have a wide variety of experience in varying dive environments?
3. Does the instructor teach On the Side part-time or is s/he a full time instructor. Ask him/her why do they teach cave diving.
4. Ask the instructor to explain the gear configurations s/he will require, and ask if there is any flexibility in the acceptable configuration. (In many cave instructors opinions, mine included there is more than one configuration that works. Some are dogmatic. Stay away from dogma.
5. Ask the instructor to explain the scope of the cave diver training s/he plans to provide for you. They should be able to explain the overall program goals as well as the details and day-by-day, dive-by-dive schedule of goals, and milestones in the training process.
6. Ask the instructor about fees; make sure you understand ALL the fees. This includes books, e-learning, certification materials, gas fills (Nitrox or air), park entrance fees, and gear rental fees such as tanks.
7. Ask the instructor to give you suggestions on lodging.
8. Ask the instructor which dive site(s) you will most likely dive in.
I think once you ask these, and other questions you may come up with you can be in a better position to choose your cave instructor.
What about after the class
After the class begins do not be afraid to ask the cave instructor to justify why s/he has suggested a certain gear configuration. The instructor should be able to provide you with a logical reason for each and every gear configuration they have asked you to make.
I do not mean you should challenge them per se, but you must understand the reasoning for all the nuances of the way your gear is now configured. Do not just follow blindly the gear configuration your instructor asks you to make. Be a thinking diver; do not just follow a set of rules because they are there. Do not be dogmatic.
Ask the instructor what each exercise and/or drill you are doing is designed to help you prepare for.
Most likely if you have wisely chosen your cave instructor s/he will use time tested and community wide agreed upon gear configurations and training techniques.
There have been lots of gear changes since I taught my first cave diving class in 1975, but one thing that has not changed is the mental attitude required for a diver to become a safe cave diver. I would rather dive with a cave diver who has old gear and a safe attitude than with a cowboy, with a macho attitude who has all the newest gear available on the market.