I completely forgot to answer your question for suggestions on blocks. I think something with curved seams would be great to add to your repertoire. Curved seam blocks include Drunkards Path and New York Beauty. NYB is usually paper pieced to get those nice points so you may be able to tackle two new skills with one block.
Something with set in seams (aka Y seams) would also be a good addition. Blocks that include Y seams are LeMoyne Star, Attic Windows and Tumbling blocks.