to avoid the Cenotes for first trip anyways. My first two dives after doing my certification dives in a cold Colorado lake were into the Chac Mul cenotes near Playa del Carmen.
While my dives went just fine and I actually enjoyed them, had I not been so ignorant at the time to the fact our guide not only took me as a brand new diver (yes, I made them aware of my lack of experience at least), but alos went beyond what is defined as cavern vs. cave diving I would have sat out the dive altogether.
I am a bit of a fish and it takes alot to spook me, so I enjoyed the dives with no problem, but consider myself lucky to have done so. I do suggest going cenote diving once you have some more experience and have found a Mexican dive operator you trust. Expect to get into VERY dark places, close quarters, and come to grips with the reality that the definition of cavern diving is often not strictly adhered to. While I think that cenote diving is a great experience, there is only one divemaster in Mexico I would cenote dive with without being cave trained.