1. Factions.
This is just a fact of technical diving society, sorry! People sort into groups based on their philosophies, preferences, and priorities. It's worth it to spend some time talking to people within different groups to see if one resonates with you. For example, some people totally love the GUE philosophy and live it, and other people prefer the do-what-works approach.
2. Small community...
This is just another fact of technical diving society. Only about 1% of new certs each year are for technical diving (
TDI) and there are probably only a few thousand people who are
actively cave diving (
CaveDiving.com). We're probably all within three degrees of separation.
3. Strong Opinions/Personalities
This is just a diver thing.
4. Logistics
I agree with you here: there are many different forms of cave diving (Mexican cenotes, Florida high-flow caves, Ozark mudholes, English sumps, etc.) and they have different skill demands. The best approach is to consider what type of cave diving (a) you want to do and (b) are most likely able to do. Think about whether it makes sense to train in Mexico if vacations to Florida are what you can afford. Think about whether you'll want to deal with high flow, complex navigation, bad visibility, etc. It's important to find an instructor who is prepared to teach you what you need for the kind of diving that you want to do.
I chose to train in Florida for two reasons. Firstly, I can drive to Florida in 1-2 days for vacation and that helps me go more frequently that I can get to Mexico. I can also bring my own preferred gear in the car. Secondly,
what I was told is that people who learn to dive in Florida can adapt to Mexico easily (conditions are usually less challenging), but Mexico-trained divers have to put in work to learn how to dive in flow.
5. Instructor Choice
This one is more challenging for people who aren't local to their diving caves. I've been quite lucky that Reggie Ross (who was recommended to me) and I got along very well and now that Chris Brock has taken over my training, we also have a great learning relationship and friendship. I'm ready to recommend Chris to you right here, right now. I'd even be happy to have a phone call about it and put you in touch with him.
When you're picking an instructor remotely, anyone credible is going to be willing to spend time on the phone or on Skype with you. Cave diver training is a serious commitment that goes both ways - they also want to know that they're a good match for you and your needs before you start dropping $300-400/day on training. You'll have time to ask about their training methods, philosophies, preferences, etc. You can also ask them to provide references from previous students and make separate calls.
Cave diving instruction is a very reputation-based industry. You'll be able to find out a lot of information about instructors from general internet searches, reading here on ScubaBoard, asking people on Facebook (there are several highly-active cave diving groups), and making conversation.
When you're starting to look at instructors, feel free to ask us here. I'm certain that SB has divers here trained by all of the "public figure" instructors, many instructors who are less prominent in the community but still excellent, and by instructors that you shouldn't step near.