@Diverspoint I'd be interested in finding out what you mean that Chac Mool is contaminated. I was diving in Chac Mool in May and found it to be a really nice dive.
@laikabear Regardless, Chac Mool is an okay dive. It is nothing special but if you never been cenote diving, it is a good dive to start with. Chikin Ha is also another good first cenote to dive.
If you have trouble equalizing or ear troubles in general, avoid Taj Mahal. There is a lot of up and down in that dive. I'm not great at equalizing; it always takes me a while to get my ears to clear. Taj Mahal was pushing it for me. At one point I had to signal the guide to give me a little time on one of the descents.
I really liked Dos Ojos and the bat cave in that cenote.
All these dives are good beginner dives. I don't know if 'not cavern trained' means you haven't been cenote diving before. If you haven't been cenote diving, these are good cenotes to begin with. They aren't as advanced and if you haven't been cenote diving before, you'll still be impressed with these cenotes.
For all these cenotes, try to get there early. Because they are good for beginners, they can get a little busy. Once you get some novice divers in there, they tend to silt up the place. When I went to Taj Mahal, it was REALLY early in the morning (I was staying just 10 minutes away). The water was amazingly clear; we were the first people there and the water was so clear I couldn't even see it until the guide slapped it.
I also went with just me and the guide. So I didn't even have to worry about other divers in our group. The second time I went there I got a discount because I'm a DM and they asked me to take up the rear and watch after the other divers.
Definitely worth paying for a private tour the first time.