I just tested some of this myself.

Recruitable generals cost 200 per turn in addition to their bodyguard fee. I didn't test client rulers but I'd assume they would be the same. 200 is the same fee a real family member costs per turn.

On large unit setting, cavalry generals will tend to provide about 40 men after being recruited, and infantry ones around 60, regardless of what they say in the recruitment page.

I dont know whether the generals/client rulers affect your max amount of family members or not.

The cav generals are really useful since you get alot more men in each unit than you would with a typical family member general, plus they passively replenish their numbers after each battle.