What is the optimum player position respective to mob grinder?

Mobs won't spawn closer than 24 blocks. They won't move around when farther than 32 blocks. Those are the only rules you need to know for a grinder that relies on mobs walking around.

The inference is straightforward: you want your collection spot to be 24 metres away from the nearest wall of the grinder, and you want the far wall of the grinder to be 33 blocks away.

Or put another way, you want your grinder to be in the 8-metre-thick ring or shell around the player where mobs will spawn and move. In this illustration of the spawning distance rules, this thin shell of viable spawning area is represented by the light blue ring:

This implies that the optimal grinder is shaped like a ring or a ball surrounding the player. (Note that these distances are true radii, so if the grinder is above you in need to be closer than 24 horizontal metres!) Construction considerations make such a design less than optimal though, so a nice compromise is one to four towers that each fully enclose a section of the useful spawning shell; even if some of the floor space is "dead" sometimes, the less-perfect design allows you to move around in your collection zone a bit more and still have the grinder(s) work well.