I awlays check the succession order when any heir is of age.
Soon as I see anyone less worthy above the best prince I have I send him on a suicide attack against 2-3 stacks of my eenemy somewhere - an island if possible, until he dies in battle.
This, coupled with always using my king in enough fights to get his stars up high, marrying princesses into and out from my faction (latter to strengthen alliances, former to produce good heirs), creating high influence by immediately taking some real estate and doing a crusade/jihad as soon as a king is crowned seems to produce really good heirs for me.
This has increased my economic standing so well that my trade empires rake in florins every game under great kings.
Sets the tone for the whole game really.