Sorry I got somewhat carried away.
So back to topic...I think it was already discussed by many what their aims are (overthrowing their father/brothers/sisters, becoming a schoolar, changing the social norms etc), but what are your (question for everybody) preferred strategies for that? (I think that got also discussed...but you never can scheme too much)
My MC most likely will try get into a position as adviser to get the kings trust and to avoid getting married off. From that position it should be possible to gain allies or to at least convince the important people (in the military etc.) that MC may be the better leader. That hopefully will gain MC enough support to slowely put the king/MC's brother(s) out of the government, making them puppets for the public to cheer/blame, while MC gains the power and slowely changes the country after their vision.