I would avoid Devil's Throat. It is a swim-through that comes out around 100' and is more of an "I did it" dive rather than "super cool" IMO. I have been to Cozumel many times, never interested me enough to go try it.
You might ask about diving the wreck there (C-53 I think?). It's a neat dive but sometimes currents can be strong. I got lucky and there was almost no current when I dove it.
Looked in my log books - Devil's Throat comes out around 130 - 140 feet - way too deep for a beginner. I've done it three times, once because I wanted to experience it, and twice more because others on the boat wanted to do it. I would rather stay shallow and enjoy the life, while at the same time having a longer dive.
I have dove the C53 once and wasn't really impressed, perhaps because I am spoiled by the life on the artificial reefs here on the west coast. I would rather do a night dive at Paradise than dive the wreck again.
As others have said, hiring a private divemaster, no matter what op you choose, will be a wise investment.
For a really neat outing make sure you get down to the main square in San Miguel on Sunday night to experience the festive music and dancing. I'm confident that you will be bitten by the Cozumel bug once you experience it. I know I was "bitten" after my first trip to Cozumel in 2009
Dive safe !!
Divegoose