You might want to use an operator selected by the cruise line. Cozumel is famous for its underwater currents and fantastic drop offs. I've seen lots of variation among the local operators and their equipment. Long ago I had a very dangerous experience with Blue Bubble, their equipment, and a disappearing boat operator. Doesn't mean they are bad now, though. Lots of turnover at these dive shops.
Last year I had great dives with Aldora, but they use extra big tanks and only take very experienced divers.
Aqua Safaris runs a big operation that might be worth investigating.
My best advice is to talk to the on-board folks. On my first cruise the activities director introduced me to a slot machine repairman. Turned out he was ex-Navy diver and we had a great dive on a wreck in Barbados.
Most importantly, Don't be shy about your experience level. The worst thing you can do in Scuba is keep head colds, nerves, hangovers, or other problems a secret. Be up front, be conservative, and enjoy a great sport. (I've been diving safely since 1979 across the Caribbean.)
Just remember the time change from cruise time to island time if booking with a dive company in cozumel. When we booked an independant dive there was a mix up with the time. I developed a sinus infection and could not dive and my husband still had to pay for my dive. Make sure you get all the facts straight first. He did say that it was a wonderful dive. Great sea life! He saw an eagle ray. I'm so mad that I missed it.