Tip for the above: Don't marry the first few generations of daughters into other courts for diplomacy. Instead marry them so their children are of your dynasty to both foreign and domestic geniuses of any rank so they make a lot of courtly, dynastic, and possibly genius babies.
If you do this, you should have a whole bunch of descendants of your dynasty. You should also use the character search thing to find the best martial person you can find to educate some future war leaders and teachers from your area, including a son if you have one way down on the inheritance pole.
First check for the possibility of inheritance in your surroundings, especially with big powers. Sometimes it's worth it to spend large amounts of gold on effecting the chain of succession in neighbors if you can get a dynasty member into inheritance with a pre-arranged marriage. Marry a daughter or other female dynasty member to the 4th+ or whatever the most eligible son is and assassinate whatever sons the the RNG does not. After the actual inheritor dies, his title is suddenly controlled by your dynasty.
Really, the FUN you will probably run into is that the king you are playing as will linger a long time after the heir reaches maturity. One way succession might not go the way you planned is that you might end up with the heir in your court being assassinated easily because he doesn't control any land. If you give him land though, he is able to pick who educates his own children, which results in wrathful, greedy, gluttonous rulers when the line of succession reaches that particular spot.
I'd kind of like to start a new game as Poland and focus on Russia this time instead of Jerusalem and try to get me an Empire for once, but then again there is that new update coming out...
EDIT: Maybe also I should try educating into intrigue instead of diplomatic masters for rulers. I also could use more gold to turn Poland and everything East of it into a fortress against the Mongol Hordes. Building only cities and improving them and other income buildings wasn't enough by itself to be able to afford necessary mercenaries while being stuck with rulers with poor money generating ability.