What gives tube amps their warm distortion? The preamp tubes or power tubes?

[Feanor]

I have always used transistor amps to play guitar through.
But I'm about to buy my first tube amp.
However, there are all tube amps, hybrid amps that have just a preamp tube, and hybrid amps that just have power tubes, and it's kinda confusing. I want to get the sound of an overdriven tube amp, but which tubes give you that, the preamp tubes or the power tubes?

Others might jump in here, but I'll say what I know.

First, do you really want the "overdriven" sound for hi-fi playback. Guitar amps are a different matter because their effect is part of the sound production, but playback back is REproduction.

Single-ended tube amps are popular with some folks because they produce almost entirely 2nd order harmonic distortion which is pleasant to our hearing; the more common push-pull tube amps produce more 3rd order harmonic distortion which is still inoffensive but less so than 2nd order.

OHOH, solid state amps typically employ a lot of negative feedback which creates higher orders of harmonic distortion but less distortion overall. Despite typically lower distortion overall, lots of people are apparently sensitive to even very small amounts of high order distortion and/or they like a lot of 2nd/3rd order -- I'm not sure which.