snapper and grouper
Never fished in Mexico but have caught lots of snappers and groupers. (In FL where I am from, also did numerous trips to the Dry Tortugas and several to the Bahamas)
As for rigs, names of rigs can be confusing depending on your geographic location. In the south they actually call the rig with the egg sinker the fishfinder rig. (Probably different other places) but that is the rig (egg sinker to swivel, leader, than hook) that works best. If the area is not fished real hard and I imagine it isn't, all rigs should work to some degree. Groupers will eat just about anything.( Live/dead/bucktail jigs/ diamond jigs etc.) If they are there and hungry it should not matter. As for the snappers (again depending on fishing pressure) they tend to be more particular (at least in some situations) Flourocarbon leader is a big key with the big snappers, Hooks depend on the person but I like either a large ( 4/0-6/0) kahle style hook or a circle hook but again it should not matter too much. Use just enough lead to reach the bottom and that is all with roughly 6 feet of leader. (leaders can be quite a bit longer if you are drifting.)
As for baits, while live shrimp certainly will catch lots of fish, for the big dogs you want a big bait. The macks they catch on the party boats this time of the year here would be perfect. (Not to take them there, I am just using them as a size reference.) There should be some type of local bait (scad/gogeleye(sp?)) in that area that will work fine. (even grunts work great, the main thing if you can help it is fresh rather than something that has been frozen.
Another option would be to put a trailer hook on a bucktail jig ( again just heavy enough to reach bottom) and attach any large strip of bait (anything including barracuda bellies/strips etc) it does not have to be pretty.
bounce this rig off the bottom and you should do well on both species.
I would imagine the fishing in Mexico is similar to the fishing in the bahamas in that the fishing is so good it won't matter too much what you do. But it is fun to target different species. (on one bahama trip I used the bucktail with strip rig I described. In less than 2 hours I caught red and black groupers to 26#, several nice mutton snappers up to 15# and a 25# wahoo that hit the jig on the drop. Again different water but very similar type of fishing.