I find the kingdom starting process actually easier as compared to native, and way more interesting.
It takes many long preparations of course.
Build relationships with lords of other factions to recruit them as your vassals in future, build relations with kings of factions and the Pope. Gain renown and right to rule.
As soon as you have at least one village - expand your manor. Invest in regional manor, build all kinds of enterprises there and gather taxes in goods from some of them, this way you have access to nice goods for sale or sending out as gifts.
Building some improvements to your regional manor actually gives you right to rule which is the key to recognition as a legitimate faction in future!
Go to the village and build village manor in it. Then fortify, and you have your own castle! As soon as you have a castle, you have staff, which allows you to send gifts to lords. This is where your manor enterprises come handy. Gather taxes in goods from:
- oil maker
- winery
- brewery
... and send gifts to other lords and kings.
Expand your dominion, obtain control over more centers (high renown improves your chances to be granted more fiefs), buld more regional manors, improve your finances and rep.
AND WHEN it comes to indepence, you gather armies from your regional manors (to hell with their prosperity, let those dirty angry bands of alcoholics go to war in your name!)
and as soon as you declare yourself a king, send an emissary to the Pope Alexander IV with a request to crown you! Granted that you have a good relationship with him, (and right to rule, maybe?) he will declare you a legitimate king! The moment he does, you become recognized by many other factions as well which is key to survival as a faction.