I always thought that the 'th' in tuatha was pronounced the same as 'th' in English. I may be totally wrong (probably am), but I'm thinking in terms of Irish, and I assume what Beloit Piper has given is based on Scots Gaelic, except where he says otherwise. As he says, there are differences. Now I'm curious if the Irish pronounciation is tooha like he says or if that's only in Scots Gaelic?

I think tuatha means a chief, or in the Irish context a minor king (in some cases that was the same thing), but traditionally Ireland was settled by the Firbolg (or Fir Bolg), then the Tuatha de Daanan (spelling?) and then the Milesians (from the Gaelic branch of the Celts) in that order.