It has been said before that as a "rule of thumb" any of the Cozumel Dive Ops with Blue in the name are good!
I have used Deep Blue on two separate vacations, and I know some friends that have used them numerous times in the past. We have been very pleased with Deep Blue. Of course, I have no other Cozumel experiences to compare to, but I would definitely use them and recommend them.
They bill themselves as "Extended Range Diving" and they definitely can handle experienced dives and divers, but they also instruct. Some places may have more experience with newbies, but from my experiences, the Deep Blue Instructors are good.
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I suggest that the single most important thing (regardless of what dive op you select) is to be up front with your situation: Let them know that you are a newbie, what fears or concerns you have etc. Most dive ops will try to accomodate you, but only if you communicate with them. Neither your nor the dive op wants any "surprises".
Don't be afraid to ask questions if you are not sure about something. Many divers in Cozumel are "Repeat Offenders" like myself. We kinda know what to do, where to go etc. Some newbies watch out of the corner of their eye, and try to follow along. When in doubt, ask.
Relax and enjoy!
Wristshot