In a way, cities are simple to garrison because militia availability makes the choice easy. With castles, I'm less sure about what to do. There's no free upkeep, and public order issues are generally less pressing.
In my Sicily campaign, I've often used Muslim archers (often two units) as a garrison, because their upkeep is fairly modest (125 florins), they can do good damage in a sally or shooting from the walls, and they're tough enough in melee to hold the walls somewhat against ladders or siege towers. If I see serious opposition on the way, I'll sometimes more stuff (sergeants, Norman knights). I'll sometimes also have Italian spear militai in my castles, since they're about as good as sergeants but cheaper to maintain (125 instead of 155), or pavise crossbow militia since they're so cheap to maintain (100 florins) and powerful. However, inability to retrain militia in a castle is a hassle.
What's your approach? I've heard some people just like to station a unit of peasants in their castles, which is the minimum so that they don't suffer the public order penalty of having no garrison at all and can't be taken by the enemy just walking in without even constructing siege equipment, but no need for a more significant garrison than that.