The June Block of the Month is a pinwheel variation. I saw this in a quilt on line the other day and immediately loved it - I hope you feel the same way. Instructions produce a 10.5" block, with minimal seams and no y-seams to worry about.
I'm suggesting a grey background, which should be the lightest of your 3 fabrics. A dark(ish) in the center of the pinwheel and a medium (preferably something bright) for the outer portion of the pinwheel.
You can find the directions here.
Bring your block to the June meeting for the draw, and the winner will take home the whole set.