A few requirements before you start..
Join
DAN: Divers Alert Network - Scuba Diving and Dive Safety Association and get their Dive Insurance. Don't even think of getting wet without membership and insurance. Insurance costs vary with states as they have to get changes approved with each one, but if you see a choice for the $30 insurance for your state,
reject that one. Get at least the $40 insurance, $75 with membership, per year. I have the $75 insurance, $110 total, per year.
Get a couple of bottles of Swimmers Ear drops at any drug store. I make my own with equal parts vinegar & 50% alcohol plus a squirt of glycerin, just made a 4 oz batch for 3 bottles for my trip tomorrow. Use it after every dive and every shower on a dive trip, without fail. Otherwise you could end up in a doctor's office on the verge of tears like my last mistake years ago, and diving is over for a week. That recipe breaks down after a month, so repeat for any trip, but it's almost free.
You're going to want your own dive mask that fits your own face well & comfortably, and you may want your own snorkel, but don't spend much on the snorkel as you'll never use it in real diving. Just get one with a drain valve & a keeper. I keep the ear drops in my mask box, another in my bathroom bag. A small dropper bottle of baby shampoo is also good in the mask box for defog on the mask.
Search for
scuba equalizing, watch some videos and be sure you can ok. Better, watch this hour long video, the best out:
I'd also get some original formula Sudafed (behind the counter, show ID). I use Wal-Act D from Walgreens. It's not legal in Mexico tho, and I don't want you to get busted. I always hope I don't; haven't yet. I don't leave home without it.
Shop for flights & in town hotels now and buy no later that September. I'm good at that, but I don't know where you are or how nice of a hotel you like. Consider trip insurance as your medical coverage may not cover international, etc. I like Travel Safe
classic plan, not their cheapest, but there are other good choices.
I don't understand why some suggest doing class & pool at home, then getting a referral. More expensive, more details to keep up, more opportunity for things to get lost. Doing the online studies at home is certainly the way to go, but doing the class & pool work on vacation is not that big of a waste. You have to do the four check-out dives on two different days anyway, so do the class & pool work mornings. It's two days, either way, so do it all in Cozumel. I'd rather do the class, pool, and open water with the same instructor.
I've dived with a lot of operators on the island, most good to better as it's a competitive market. Just avoid the big boats that cater to cruise boat divers. I am very pleased with my current choice, and I've known the guy for years before he moved to Coz so I'd insult him personally if I wasn't.
He is the most thorough I've tried yet, and I'm sure his training is great too. His prices are certainly competitive @ $450:
PADI Dive Certification - Learn to Dive Today! | Salty Endeavors Email him with any questions about class size, open water, etc. I'd rather do the check-out dives from the beach tho.
After you get your card, hire a private DM for your first two tank boat trip. Money well spent.