Signal tube versus power tube, sound impact?

I have noticed more difference changing the output tubes.

Power tubes first, small tubes to fine tune. JJ power tubes are OK if you like them. I use their E34L's in a small amp in preference to some other excellent tubes. Power tube selection can make a big difference in the sound so the first thing you need to do is try to define what sound you want to hear. While tubes do interact with your amp to get this sound power tubes do have a intrinsic sonic signature (as do small tubes). FWIW new production tubes are generally good, NOS power tubes are exceptionally hard to find and very expensive. 

Likely only 1 preamp gain tube  in each channel will make a noticeable SQ difference. Could be subtle or quite noticeable.

If your amp accepts different model tubes-EL34 for example, it will be a noticeable move. YMMV, but typically enhanced mids/less bass with EL34.

Look up what other type will work and their sonic character.

Going on about 30 years ago I spoke with Andy of Vintage Tubes (in Michigan) with basically this same question. I was interested in retubing (with NOS) a pair of ARC VTM 120s (6922s and 6550s) and a Cary SLP90 (12au7s).  Andy's advice (which I followed) was to start "closest to you" which meant the preamp and then the signal tubes in the amp.  The improvement in SQ was significant.

A few months later down the road I talked to Andy again about output tubes, and he wound up selling me a pair of quads of NOS Tungsols (not the Russian reissues that are out there now) to replace the Svetlanta 6550s I had in them.  For as much money as I paid for those NOS Tungsol 6550s I was expecting a huge sonic dividend and I was disappointed.  I really didn't hear any improvement.  Maybe because I was expecting too much?

Anyway, going by that experience and Andy's advice, I would start replacing tubes from the front and work backwards.  And I have heard good things about JJs for the price.