Welcome on board act005
I can't comment on the diving off the Pacific Coast as I wasn't a diver when I visited there. However, I would *guess* that side in general has less visibility, colder water and more surf that the Mexican Caribbean.
The places I dove in the Caribbean are Cozumel, Mahahual (also spelled Majahual and called Costa Maya by cruise ship people) and Isla Mujeres.
The dives I did on
Isla Mujeres were really easy. Shallow, good vis, no current that I recall, lots of fish but no impressive coral.
The island, located right off Cancún, is very easy to access, lots (too many ?) of hotels in all price ranges, restaurants, shops, nightlife… Beautiful beaches as well. Great place if you like partying. If not, stay away from "town" (the North tip of the island). No cruise ship but lots of (drunk) day trippers from Cancún.
Mahahual is located much further South and has a very different feel. I was there 6 years ago (since the place was hit by hurricane Dean and is rapidly developping, it might have changed a lot), back then it was a very relaxing stretch of paradise… I stayed several miles south of town, so wasn't bothered by the cruise ships (except for the 5 minutes when the ATV group roamed in front of my hammock). Not much to do besides diving, snorkeling (which you can do from shore) and other water/nature activities. Shops were mainly open when the ships were in town. You can visit ruins and go to secluded beaches if you rent a car.
That's where I got certified. Most of the dives I did were 5 minutes from shore on a small boat and between 30 and 70 feet. Great vis, little current, very easy. The reef was beautiful, lots of healthy fans and corals back then (don't know if that has changed) and a good variety of fish and other sea life. I think I had 3 turtle sightings in 2 weeks of diving, though. That also could have changed a lot. One way or the other.
Here are a few pictures I took a couple miles South of Mahahual in 2005 so you get an idea of what it looked like :
http://picasaweb.google.com/annlaur75/Mahahual2005?feat=directlink
There are some nice hotels/bungalows on the beach, and a few very good restaurants, but as you can see it is still pretty remote and quiet.
Last but not least :
Cozumel, aka the dive Mecca of the area.
The visibility and coral architecture are amazing and it offers a great diving experience. If you dive Punta Tunich/Yucab (usually a 70 - 50 feet depth dive, if I recall correctly), you are more than likely to see a turtle or two or more. As a matter of fact, I think I saw a turtle on almost every diving day in Cozumel.
The downsides are that the currents can be swift (not that big of a deal, but drift diving, while very enjoyable, takes a bit of getting used to). Also, most ops do 2 tank morning dives, with the first typically starting below 70 ft (sometimes below 90 ft), which is where the most impressive "coral mountains" are. There are swimthroughs as well (short tunnels through the corals) that many people love to dive through.
With your experience so far, you probably shouldn't attempt those dives. Staying 20 feet above the group or going around the reef on your own while others explore a swimthough is not an option because the currents might get you separated.
You are wise to consider hiring a private DM, but you should also research your op carefully and make sure their boat will take you to the shallower reefs on ALL dives.
Now the upside is that Cozumel has a lot of dive shops, so you're likely to find one that suits your needs, professional DMs and instructors, several recompression chambers on site (one never knows), divers everywhere so you can easily meet people with common interests.
The island itself has something to offer for almost everyone, with a very touristy waterfront (full with duty free shops, cruise ships, bars…
, a very Mexican town with great restaurants and friendly locals, all inclusive oceanfront resorts away from town, and a beautiful wild (East) coast with sandy beaches and heavy surf.
Of course I haven't included all the options for diving on the Caribbean, only the ones I personnally experienced. And this is just my opinion. You might also want to research Puerto Morelos, Playa del Carmen, or even Cancún.
Considering you are new to the sport, I'd suggest you don't necessarily look for the most beautiful reefs right now (I'm sure you'll have other opportunities to go dive in Mexico), but focus on your comfort level and on what you are looking for in your vacation besides diving.
Wherever you end up going, I'd also suggest doing a refresher. You can do it in the pool at your local dive op, but doing it with your private DM will give you an extra opportunity to get to know each other/voice your concerns in a very safe and easy environment and it will give you a feel of the local diving conditions regarding current/vis/water temp/equipment if you're renting/your weighting…