Where are you staying? Often that will determine the dive operator you will use.
What to expect?
Drift Dives, there is some shore diving available but most of the dives are boat dives
Great visibility, the visibility there is often 100'+
Warm water, 80+ in my experience there.
2 tank morning dives are the norm
Plenty of life to look at underwater
Friendly and helpful people, I haven't met anyone there that wasn't friendly
A safe, clean island. Never went anywhere on the island that I didn't feel safe
A variety of dive operators from bargain to boutique, I can suggest Blue XT Sea for a dive op. Great service, recent boat renovation
Plenty of other activities you keep even non-divers occupied
Lots of great places to eat. If you are staying at a AI resort you may still want to venture into town and try some of the food that is offered
IMO Cozumel is a great destination for the first dive trip.
I am sure others will be along to expand on things but that (for me) is the quick list of what to expect.