I know many are here.

I am a yank...

I have no idea where to begin to ask about it, other than Loreena McKennit

How can I learn the music of my Celt ancestors?

I don't even know if my forebears were Scott or Irish

All I can tell you is that my great ancestor was named "PURDY", which doesn't seem an irish name

Look for anything done by The Chieftains, they're about as traditional as it gets and have been around for decades. They have lots of albums you can no doubt find in your local used music store.

http://en.wikipedia.org/wiki/The_Chieftains

There was a thread about celtic music back in June, which you also posted in. That would be a good start.
http://www.gamesas.com/topic/1502163-celtic-music/

try the Dubliners or the high kings or even great big sea

river driver, red is the rose, whisky in the jar

Take a look at some Sean Nos music. That's actually as traditional as it gets. Caitlin Maude is an excellent place to start.

As mentioned, you should read through the http://www.gamesas.com/topic/1502163-celtic-music/ to start with. (which you also posted in)
That seems like a good place to ask for suggestions.

We only need 1 thread for a genre.