face turning octahedron- these are great for teaching yourself about commutators and conjugates. This and the master skewb

curvy copter

any 3x3xn cuboid such as the 3x3x6

axis cubes are fun.

skewb

Overall, I would recommend buying some non-speed cubes to expand your horizons. If you want to try out a cube before you buy it, use ultimate magic cube. The first one can make pretty much any puzzle in the shape of a platonic solid(no shapeshifting or jumbling), but the second one has some shapeshifting and jumbling puzzles in it. If you have any questions about the program, message me, or I'm sure you can find some sort of tutorial on youtube. Most puzzles you would want have to be user made.

edit: more suggestions:

megaminx

mastermorphix