[prawn]

If you want to get a cube to muck around with, don't frustrate yourself with something default - either pull apart and lubricate one of the standard ones, or pay a little bit more and get something used by at least keen amateurs. The cheap ones are pretty miserable to use.

I have one of these and it's smooth: http://lubixcube.com/lubix_dayan_guhong_v1.html

Bad Mephisto has already been linked elsewhere - he has some really helpful videos and a cheatsheet to refer to.

[Bognar]

I highly recommend any cube from Dayan, but this is my favorite:

http://www.amazon.com/dp/B008U6V50U

It's smooth as butter, and there are no stickers to cheat with.

[captn3m0]

Stickerless cubes were until very recently illegal in competitions. The new regulations (in effect from July 2015) allow these now, meaning a stickerless Zhanchi is a really good purchase.

[torrent-of-ions]

Yeah and get one with plastic stickers as well. The Rubik's brand ones begin to look disgusting before long.