Our first dives after certification were in Cozumel, my youngest daughter was 12. With 4 divers, it may be just as cheap to charter your own boat. Many of my favorite dive sites can be managed above 60 feet. Frankly, above 40 has the best color and often the best marine life. I could dive all week and be happy diving relatively shallow. Long dives with lots to see....what more could you ask.
Our first dives were with Dive With Martin and could not be happier with the experience. We dive with Aldora now, but Tres Pelicanos and Blue XTSea have an absolutely rabid following here so they must be good too. I have also dove with Blue Magic and can recommend them without hesitation. There are lots of great ops on the island.
As far as where to stay...we like staying in town at Casa Mexicana. No beach, but we get our beach time on the surface interval. The all inclusives are mostly down south by the common dive sites. Staying there means shorter boat rides, but a longer cab ride to town. We LOVE town. The square and all the great food makes an all inclusive a waste (my opinion). We stayed at Sunscape Sabor last March and I wasn't impressed. Food was mediocre, service meh, and a long ride to town. Just not my thing.
Every choice will have a trade off. Contact the dive ops and check on a private boat. Your boat, your schedule, your choice of sites, no other divers to worry about. It worked great for us and was around $400 for the day. I'd bet you could get a better deal for a multi day charter.
Good luck, safe travels,
Jay