Having just finished reading the LOTR books, I'd have to say that more the English style ales. Browns, Porters, Bitters, etc.
There was a small part towards the end talking about a certain grain that grew exceptionally well to make good ale. But that's about all it goes into.
They smoked fine tobacco, so I would assume any good ale that goes with that. I don't smoke, so I have no idea. Brown, Stout, Bitter?
I remember reading/hearing something that likened the Hobbits to the Welsh (or Irish), Dwarves to the Scotts, Man to the Brits, and Elves to the French. So maybe that helps??