Certainly the three books to consider are Howell and Webb for Mexico, and either Fagan and Komar or Vallely and Dyer for GT (and the Yucatan). For the latter two, they're honestly both excellent books. Perhaps Vallely & Dyer has a bit more information available but on the flip side, as pointed out, Fagan and Komar is more compact and has less extraneous species.
I don't know of any apps that cover the area, unfortunately, and haven't ever used Merlin much, so can't comment on that.
For bird finding, the old Howell book to Mexico is still quite useful, though I am pretty sure it is out of print, and doesn't include some newer sites, while some older sites have changed/degraded/etc, of course. I think you are going to need to use eBird's target species feature, hotspot explorer feature, and trip reports to put together information. Fortunately there is a LOT of info for Mexico and there aren't really any top-secret species / hard to find info.