the more play in the turbo shaft the more worn the turbo is; i believe it to be the bearings in the turbo which give the play

side to side movement (few mm) is fairly common place in most used turbos, so as long as its minimial dont be over concerned

if you can move the shaft in and out of the turbo (Pull towards you and back in again) then steer well clear.

Generally all turbos will need a rebuild at some point during their life; due to their purpose. Just try and find one that has documented evidence of being rebuilt