What title should claimant to have to remain my vassal after supporting his claim?

if your vassal gets a title that's lower than your primary title, he will remain your vassal. If you press a claim for someone of your dynasty and the unlanded kin gets a title lower than your primary title, they wil become your vassal. The only thing to consider is that mayors who get a duchy will make them a republic. In your situation, you want to press the claim on the duchy, not on the kingdom.

As long as you press a claim for someone who is your direct or indirect vassal, that person will remain your vassal.

In the case of the bishop, the claimant will remain your vassal as long as the claimed title is lower than your rank. If you're a duke and press a claim for a duchy, the new duke will go independent - so be careful.

A thing to note, if the bishop becomes a count or duchy level title holder, the county or duchy will become a Metropolitan or Prince-Bishopic respectively. Those kind of landholders provide lots of piety but very little taxes (since the money goes to the religious leader usually)