We may be an exception but we did our first dives at Cozumel and had a fantastic time. We completed our OW in August and booked a trip to Coz in October.
We purposely selected a dive op (Papa Hogs) that used small boats (6 people max). I exchanged several e-mails with them in which I explained that this was our first dive trip. They assured me that they would make sure to group us with other beginners and the dive master would take it slow with us.
Incredibly enough, when the boat came to pick us up on the first day, we were the only two divers on the boat (along with the DM). While there are deep dives in Coz, there are also many wonderful shallow dives.
Our first dive was Palancar Gardens where we did a max depth of 47 feet with an average depth of 34 feet. Our second dive was La Francesca where we did about the same depths. We were nervous at first but all the training had prepared us nicely and we had a wonderful time.
The next day we did a different part of La Francesca with a max depth of 61 feet (avg 48) followed by Paso El Cedral (56 feet max, 42 feet avg). Day 3 was Palancar Horseshoe (74 feet max, 49 avg) and then the area between Dalia and Cedral Pass (61 feet max, 43 avg).
By this time we were enjoying ourselves so much we did an afternoon dive on day 3. On day 4, the first dive was Columbia (85 feet) followed by Columbia Shallows (32 feet) followed by our first night dive to La Francesca (43 feet). We continued on to dive for a few more days (including another night dive) before heading home.
So as you can see, we started the week shallow and progressed deeper as our comfort level and skills allowed.
As for the drift diving, we found it to be easier than Bonaire (we did a week in Nov 2002). You slipped over the side of the boat and dropped down to the bottom. Then you just floated along until it was time to surface. And when you surfaced, the boat was right there. What can be easier than that? Since there were no walls, you did not have to worry about going too deep. You just stayed a few feet above the bottom.
There was no checking the direction of the current, starting the dive into the current until your air reached a certain point, then swim back for the same amount of time before looking for the boat. We could concentrate on getting comfortable with watching our gauges, keeping an eye on our buddy and working on bouyancy skills.
I respect the opinions of all the much more experienced divers above. But I wanted to share our experience and encourage you to not necessarily rule Coz out for your first dive. But it would be good to go with a good buddy. And find a dive op you really can feel comfortable with.
One other benefit to Coz that really helped us was the price. It ws so cheap there was no pressure on us to feel we had to dive a lot in order to "get our money's worth". We had planned to do only 2 dives a day (if that felt comfortable). We ended up doing 17 pressure free dives in 6 wonderful days.
Have fun and be safe.