You will need to have some form of reduction from the drive motor to the wheel but how you choose to do that is up to you, a gear box is not necessarily required. Traditionally mecanum wheels are done with four and the closer the wheel arrangement is to a square with an even weight distribution the better the better the performance.
for most of the motors legal in this years game, a gearbox would be necessary (probably should use 1 of the 6 cims allowed)
You could use any gearbox you want. The easiest would be an AndyMark or VexPro single speed Gearbox. Depending on whether you choose a Dead or Live axle setup, the items you would purchase to make the drive work would change.
4 or 6 wheel Mecanum? A Mecanum Drive is generally 4 wheels working independently. You could technically put more wheels. Though it seems counter productive. Omni wheels might be okay to use as additional wheel (non powered) http://www.chiefdelphi.com/media/photos/34594