All Quakers are quite active by nature, and need plenty of room to move around without the fear of running into various toys, swings or accessories.
A Quaker sitting in its cage of a perch should be able to fully extend and flap its wings without any interference. It should not have to perch in the exact center of the cage to prevent its tail feathers from rubbing against the cage bars. Neither should the cage be so limiting as to allow the spreading of only one wing at a time. It should be large enough to allow your Quaker to eat, play and engage in acrobatic.
If at all possible, the width of the cage should allow the bird enough room to flit or hop back and forth. If you purchase a large unassembled cage, make you measure doorways first or assemble the cage in the room you play to keep it in–you may not be able to fit it through the doorway otherwise!
The space between the bars of the cage should not be wide enough to allow your Quaker to fit his head through them (ideally they should be no larger than three-eights of an inch). Nor should there be areas where the bars converge, which may trap toes and beaks. Casters or wheels on the legs of bigger cages are mandatory for mobility. You may have to move them for cleaning, and you may want to give your bird a change of scenery occasionally.
For all practical purposes, avoid cages that are very ornate or have lots of curlicues. Your Quaker will become famous for getting his head and body parts caught in these, which is certainly dangerous to his well-being, not to mention the difficulty you will experience when you attempt to extricate him! Also, there is the matter of cleaning all those nooks and crannies. I can tell you from personal experience that although the ornate cages are beautiful showpieces, the upkeep in keeping them clean is time-consuming, and not at all fun!