Mo, you are a gold mine! I've just stolen "Weakest Link"- thanks!

Flora, I often play the accordion as accompaniment to my fiddling husband, and call at the same time, and it's tricky but manageable. The main thing is to know the tunes cold- it's fine to have notes on the dances on a stand at your side, but you can't bobble the music, because the dancers are counting on the music to guide them.
Some family dances I do:
La Bastringue (Great first circle dance- you can vamp the music while they're getting a feel for the figures, and teach as you go)
Noble Duke of York
Galopede (great first longways dance because there's so much time to do stuff!)
Rural Felicity (as learned from Dudley Laufman)
Heel and Toe Polka (to the tune of the Jenny Lind Polka)
A few mixers, like "Sasha" which is a Russian couple dance with its own tune and silly moves, where the couples part and seek another partner after each time thru.

Maybe we need a caller's Permathread? This is fun!