How many samples per cycle(time period) is actually enough to reproduce the sine wave sound properly?
It depends on how good your interpolation between samples is.  If you have really good interpolation, anything more than 2 samples per cycle will suffice.  This is not just a theoretical fact, it is my experience in practice using polyphase interpolation that combines 64 adjacent table-lookup samples.

If you're using linear interpolation (which combines 2 adjacent table-lookup samples in the interpolation), I would use no less than 1024 samples per cycle for a high-quality sine wave (about 120 dB S/N).