If you want to get a puzzle off Amazon, I cannot recommend the Hanayama puzzles enough.

I have the Hanayama CUBY and I love it. It's not too difficult, but I got kind of obsessed with it, making up nomenclature to describe all the possible states and then mapping all possible transitions. You certainly don't have to do this though, you could also just solve it by playing with it.

I also have the Hanayama Cylinder, Equa, and Elk. They are all really nicely made and satisfying to play with. (With the possible exception of the Elk, which tends to get stuck a little bit) I haven't solved any of these 3 yet, because I'm not very good at puzzles.