Hi,
The choice of a weighted base or suction cups is up to you. It would depend on how active your participants might be and where the hardware will rest. I suspect that a combination of both would be most flexible.
So long as the hardware is a standard joystick, DirectRT can handle its output. That said, DirectRT isn't able to send commands back to the joystick (for example, to activate vibration or other transducers). So any standard joystick would be ok.
Newegg and TigerDirect both have good selection, fast shipping and a fair return policy.
John