Noone seems to be backing BEagle up all that much, so I'll support his argument.
There is a published standard stall recovery, as well all know and love, pitch forward to lower the angle of attack and the wings will certainly unstall, use power to reduce the height loss and then recover to a climb. Works in every aircraft you could imagine.
Spinning is very different, as it is affected far more by the wing shape and the aircraft's centre of gravity, therefore the spin recovery is specific to the aircraft (hence no standard spin recovery).
For example a PA-38 POH calls for the spin recovery as follows
‘Spin recovery
1. Apply and maintain full rudder opposite the
direction of rotation.
2. As the rudder hits the stop, rapidly move the
control wheel full forward and be ready to relax
the forward pressure as the stall is broken.
3. As rotation stops, centralize the rudder and
smoothly recover from the dive.’
So very clearly lead with the rudder, as it hits the stop only then applying forward elevator. I've also flown aircraft which call for forward elevator before the rudder, or both simultaneously. Or simply to neutralise the elevator while applying anti-spin rudder.
At the same time, there are aircraft out there where if you are spinning and you simply let go of all the controls you will recover. The cessna 152 aerobat and grob 115 come to mind in this case. Try that in a Tomahawk and you will kill yourself.
So to reiterate, there is no standard spin recovery, it is very aircraft specific, so whatever aircraft you are trying to simulate you should look for the pilot handling notes for that aircraft, and if it was never cleared for intentional spinning then it may struggle to come out of a spin with the "usual" recovery technique.