Our writer lived there for a while, and I’ve visited plenty for the cave diving, so here’s my (supplemented with her) $0.02:
September is starting to look like high season (landlords keep imagining high season starts earlier and earlier every year), so if you can find and lock down somewhere earlier, that would be beneficial.
Definitely take your gear if it’s appropriate for the types of diving you want to do. Gear there is absurdly expensive compared to the US. I have friends who own a Hollis-authorized dealer and their dealer cost is almost what we sell the same gear for at retail on Leisure Pro. Rental gear can be hit-or-miss and adds up quickly.
Everyone who lives in Playa says to walk the street and have a native do your negotiating for you. It’s not a modern rental market at all, which is a real pain. Craigslist seems to have more scams than legit listings. There are a few expat groups on Facebook that are fairly active and people are super helpful for finding rentals. Our writer lived at Rinconada del Sol, not super cheap, but furnished, 2 bedrooms, did 6 month leases, and right in town.
I personally am bored of diving Cozumel, so I always base out of Playa when I go. I can go up to Cancun for the underwater museum or whale sharks (when in season), do the caves on the Playa side, dive the reefs on the Playa side (honestly not that much worse than Cozumel), go do the reefs off Pamuul, or do a day trip to Cozumel if I feel like it. I couldn’t imagine living in Cozumel for even 6 months, it’s too sleepy for me. As DjDiverDan said, it’s easy to get to Cozumel, so stay in Playa for everything Cozumel doesn’t have, then go to Coz for the diving (the only thing they have that the mainland doesn’t)
Feel free to ask me any other questions, I’ve probably cumulatively spent a year in Playa over the past 10+ years now and can ask my writer anything I don’t know