A standard omni-wheel, like the AM Trick wheels, should work for what you are trying to do. Keep in mind that when moving, unless going directly in the direction of an omni wheel, the entire wheel is turning (as well as the passive rollers).
Additionally a "holonomic" system can have any amount of wheels. A kilo-drive (kiwi drive) is a 3 wheeled variant, etc. Holonomic just basically equates to a vector-based omnidirectional system. It has a full range of 360 deg motion, and the direction of your force can be changed almost instantaneously (as soon as the motors accelerate). Holonomics suffer in other respects though. They are inefficient in terms of drawing max potential from your motors (often resulting in a low torque and/or speed). The exact loss of potential depends on the amount of wheels in the system. Additionally they require all of your wheels to remain in contact with the floor at all times to work properly. That often means that you are unable to travel up ramps, stairs, etc
A "ball drive" acheives the same functions as a holonomic drive. The motion of the "wheels" is based upon a vector of the forces applied by the two motors on the "wheel" (the "x and y axis motors"). So once again, you suffer an potential loss in how much you can get from your motors. Ball drives do not have the same problems with inclines as a holonomic drive does. Ball drives have a much smaller contact area with the floor, and often are made of a lower traction material (but if you have money/weight I'm sure you can use a higher traction ball), resulting in ball drives being relatively easy to push.
A "mecanum drive" (Jester Drive as dubbed by 357) is another omni-directional variant.
This thread has links to explain the exact mechanics of a mechanum drive. Mecanum drives, at least those in FIRST, typically have rollers placed at a 45 deg angle to the wheel. Mechanum once again suffer in losses of the maximum potential of the motors, but they typically have solid traction and can climb inclines with the same ease as a "skid steering" system, if not better.
"Swerve" drives are yet another variant of an omni-directional system. They function by having the drive wheels (typically 4) physically rotate to match the intended direction of travel. Teams 71, 118, 1261, and many others have enjoyed tremendous success with this drive style. The "wasted potential" appears again in the form of the "Steering motors" cannot be used elsewhere on the robot and do not contribute to the power of the drivetrain. These systems typically require a low traction wheel to turn properly, so the traction issue emerges again. Unlike the ball, holonomic, and mechanum systems, a swerve drive cannot instantaneously change direction, it requires time for the wheels to change direction. The biggest problem with this system is often its weight and complexity.
"Crab drives" are a system that has a 2nd set of wheels/drive motors that will move the robot directly side-to-side, in addition to its standard drivetrain. This is also typically fairly complex, and does not offer true omnidirectional motion.
I'm sure that there are omni drive systems I have forgotten, but I have done my best to describe the advantages and dis-advantages of each.