Was würdest du an meiner Stelle machen?
Was würdest du an meiner Stelle tun?
And is "an meiner Stelle" more common or "in meiner Lage"?
Was würdest du an meiner Stelle machen?
Was würdest du an meiner Stelle tun?
And is "an meiner Stelle" more common or "in meiner Lage"?
"In meiner Lage" is "in my situation / position / condition" and therefore not 100% interchangeable with "an meiner Stelle" (/"In my spot" aka "if you were me").
also "an meiner Stelle tun" sounds way more natural, though both your ideas are grammatically correct.
Source: Native speaker