Many people will say to do your academic and pool work locally before coming to Cozumel, but if you decide to go that route just be sure that the dive shop you start with locally is with an agency (PADI, SDI, NAUI, SSI, etc.) that gives you the options you need on Cozumel.
I'm neither a PADI fan-boy nor a PADI hater, but there's no doubt that PADI has the largest number of instructor options for you on Cozumel. Other agencies like NAUI and SDI may only have literally 2 shops with instructors in Cozumel, which may not work for you. Case in point, I was interested in an SDI specialty recently and only found 2 instructors on Cozumel -- and one was out of town for several months around the time I wanted to take it, and the other was not very friendly and quoted a super high price.
Just something to be aware of. And while some dive shops will still do a "universal referral" where they do check-out dives for people who started with a different agency, (1) not all Cozumel shops will take referrals from other agencies and (2) not all shops that you start with will cooperate with you finishing your cert with a different agency.