On 500mm there is little to be gained to going to bigger than 12mm for rigidity reasons, the main reason to do so would be to get a higher lead and faster traverses, but you could equally achieve this with a multi-start screw. The leadscrew should not be considered a bracing element in your machine. A ballscrew will improve efficiency therefore reducing potential for stalling out under a heavy cut and increasing acceleration (but a larger diameter screw works against higher acceleration) but won't increase rigidity (but will improve backlash).

Assuming you are currently running TR12x3 what do you see as your biggest problem?