Key Largo is a great place for a newbie to get experience, but not on the Grove. I usually suggest they go with the charters geared for them, big cattle boats, less likely to have motionsickness, with DMs in the water, doing shallow reefs.
Key Largo is also a great place for you - for, as I mentioned earlier - "the Grove, the Bibb, the Duanne, and the Eagle, as well as the Thunrderbolt and A.Busch further down the Keys Hiway."
I the town of Key Largo, there are so many to choose from, and many will offer their favorties, generally with good reasons. I've dived with several on a few trips there the last couple of years, but I'm no authority. The one I would feel good about suggesting is Ocean Dwellers, for these reasons:
(1) Nice, big comfy boats;
(2) Impressive operation, at least to my view;
(3) Often puts two different boats out each morning and each afternoon - one for newbies, one for wreck divers (I boarded the wrong one, but made it off);
(4) Nice cafe next door for lunch between trips; and
(5) Perahps important in October - WILL GO, even if they don't sell enough to make a profit on the trip.
If you do call them, please confirm that last point, and that you'll indeed be doing the wrecks you want - weather permitting. Hurricane season there, I believe.
Now, I really like the Eagle, too, but you'd need to book with one of the Taveneir DOps, same key, different town. I like Taveneir Dive Center.
My favorite motel there is the Hungry Pelican and Sunset Cove.
For the Thurnderbolt, I liked Abyss, at the Holiday Inn.
For the A.Busch, which I've only dived once, the one that seemed dependable was Looe Key Dive Center, which used to go on Saturdays and Wednesdays.
Hope this has been of some help...
don