I do enjoy the Bickersteth, John, thanks to your recommendation, though I can't claim to have read lots and lots of it or thought about it in relation to other translations. But in my opinion Dante is not an especially good way to learn Italian at first. Or Petrarch or Montale for that matter. They can't hurt, obviously, but I think the masters of prose such as Manzoni help more with getting a feel for the language. Also, children's lit can be great for that, as well as enjoyable to read, and Pinocchio is really really good Italian prose.
Andrew, I just saw your post. Do you know the Princeton Dante site? They have bilingual everything of Dante:
http://etcweb.princeton.edu/dante/index.html I honestly don't know what to suggest for the grammar. The best dictionary is Zanichelli. Also, online, the Treccani,
http://www.treccani.it/vocabolario/