So, there's a lot of REALLY good ideas going around.  I think, on ranking, I'll put in a little bit myself just to see what I can come up with.

Freshly ordained, short term title: Protoinquisitor (proto- is often used in Catholicism's hierarchy of clergy to denote something like "Vice" or "Apprentice," preluding a title without a prefix, like protodeacon or protopriest)

Shortly after learning hands-on how to do their jobs, they receive the title of "Inquisitor" (like a Marine Lance Corporal rising to Corporal)

From Inquisitor, they become (and this is stolen from the others, I like it) Inquisition Knight/Knight Inquisitor.

After that, they rise to Hierinquisitor (hier-/hiero- is a prefix meaning divine or holy, again, used in Catholic clergy titles)

From Hierinquisitor, they rise to Arch-Inquisitor, then finally to Elder or Master Inquisitor.  And if we add a rank that is the "single highest ranking inquisitor in the church," it could be Grandmaster [with or without "Inquisitor" after it]

So, in summation, it would go Protoinquisitor > Inquisitor > Hierinquisitor > Arch-Inquisitor/Elder Inquisitor > Elder Inquisitor > Master Inquisitor > Grandmaster [Inquisitor]