On the criteria for selecting a course I will say that for me the only criterion was convenience. I knew that there were different agencies, but I had no idea what the difference was or even if there was a difference. I knew that there was a "trial dive" (e.g. PADI Discover Scuba) in which I could make one scuba dive with no more instruction than would be offered there and then, and with no previous training or experience required. I also knew (or thought I knew, since the reality was different) that I would have to take my mask off and replace it under water. (I was actually only required to flood it half way and clear it for that dive.)
I don't think I was aware that I could take the pool and classroom portion of an OW course at home and finish the OW at a resort. In fact, I was so nervous about the idea of taking my mask off, and breathing while my nose was directly exposed to water, that I postponed learning to dive for several decades, though I've been a snorkeler all my life, as well as a freediver if 5 or 6 feet of depth qualifies to be called freediving. As a child I regularly dove to 6 feet or so in the pool and in the ocean. And since getting my scuba certification I've taken a freediving class as well, and have made a dive to 28 meters. 20 meters is no longer too terribly difficult for me. Scuba and freediving are very different activities, and I enjoy both. I have no interest in the extremes of either.
When I finally decided to give scuba a try I inquired about a class at the resort I was at for snorkeling on Bonaire. I checked "Yes" under "Do you take any prescription medicines" and was informed I could not take even the PADI Discover Scuba class without a doctor's authorization, so it was not until a year or so later, at a resort in Belize, where I came prepared with the doctor's form, that I took the class.
There was one dive shop on the island. There was no choice of agencies or shopping for the best price. I was there for snorkeling, and trying out scuba was a fortuitous addition to my planned activities. On my PADI Discover Scuba dive, I was so seasick by the time we reached the dive site, and had so much difficulty equalizing my ears, that I decided not to continue, but the next week I decided to give it another shot, and I did so much better that I went on and got my OW certification.
If I had known about the "resort course" system, I would have chosen my agency based on speaking with the instructors beforehand to gauge their attitudes, rather than on any consideration about the underlying agencies or costs. I figure all the agencies are adequate, and instructor attitude is what matters. I was fortunate, as I've commented before, that my instructor in Belize was very competent, and very patient with me, especially with my difficulty equalizing on those first couple of dives, and my nervousness about taking off my mask, which in the end turned out not to be hard at all.
So to summarize, for me, convenience was the only criterion: I wanted to take the class somewhere I was going to be anyway. I suppose for some people cost could be a consideration. But I figure that cutting corners on cost is seldom if ever a good idea, especially on training in an activity that poses significant risks for the untrained or poorly trained. I think my training was adequate for the kind of diving I do. And I do believe that the risk increases when one moves from recreational diving to technical diving, where a direct ascent to the surface is no longer an option.