Don, one nice easy charming tune from Cape Breton is "Da Slockit Light".
Another form Ireland is "Give Me Your Hand" and "Road to Lisdoonvarna".
Another from New England dance is "Shoes and Stockings".
Another tune from Ireland, "Brian Baru".
These are in the scope of a beginning fiddler.
I am a fumbling intermediate fiddler so I speak from experience.

All tunes can be boiled down to fewer notes until the tune is learned.

It's best to try to get a teacher who will help get a good tone with the right bow hold
and bow placement. Then go from there as you like.