I grade dances in 4 levels of difficulty (and, incidentally, 4 energy levels), the easiest having figures that shouldn't actually need to be taught, e.g. forward & back, lines cross, stars, circles, back to back, cast, arch at the bottom and everyone else through. Such dances as:

Alabama Jubilee
Bridge of Athlone
Caerphilly March (fancy clapping)
Nottingham Swing
OXO Reel
Pawnbroker
Upon a Summer's Day (Playford, just to be different)

The next one up, I show my age by calling O-level. Here we meet figures like poussette, gatepost, figure-8, any kind of hey including Rights and Lefts. But once learned, they usually work automatically. Dances:

Arkansas Traveller (Rights & Lefts)
Do-Si-Do Square (Grand Chain)
Leaving of Liverpool (Gatepost)
Serpent Without Corners (Poussette)
Twelve Reel (Reel of 3)
Willow Tree (Strip the Willow)

The other two are A-level, which need a bit of technique to make them work, e.g. by arriving in the right place at the right time, and Brainbender, which speaks for itself. Neither are normal Barn Dance fare.

Good publications are the Community Dances Manual from EFDSS, and Hugh Stewart's English Country Dance Club Book. I'd also recommend Norfolk Capers by the late Peggy Hazell, who had a remarkable ability to compose interesting easy dances. If you need calls for any I've listed, please feel free to PM me.