First off, welcome to CHR! The Healey sounds like a neat project, hope you hang around, add some pics, and keep us updated on the progress!!!

As for the questions, Lakewood, McCleod, and Quick Time are a few of the companies that make the bellhousing you will need. As for the transmission itself I'd suggest the TKO 600, built by Tremec. Any number of different companies handle them and there are also some used one's showing up on the market. There's also a bunch of different companies sell the entire "package"; transmission, clutch, bellhousing, and throwout bearing. Can save some $$$$$ that way if you do some careful shopping....