Signal tube versus power tube, sound impact?

Start with the small tubes/preamp tubes. If you go with power tubes first, you will correctly wonder if you are hearing them for what they are...and the answer is no. Marginal signal tubes fed to exceptional power tubes stands a better chance of remaining marginal. An exceptional signal tube sent to marginal power tubes stands a better chance of improving things. If you feed your amplifier the best signal possible, then you will be hearing them at their optimal. My 2 cents and most likely...you will change both, otherwise, it will feel like a Larry David skit.

I have noticed more difference changing the output tubes.

@ellajeanelle This has been my experience too. Especially recently, swapping from KT88 to KT120 (in amps that support this) effects a huge difference. Swapping between different brands of KT88 also makes a large difference, though not quite as much.

That said, yes small signal tubes can make a significant difference as well. Especially whatever tubes are tasked with driving multiple KT tubes.

Many folks claim small signal swaps are more cost effective since NOS / vintage types are still reasonably available, and these tubes can last several times longer than their power counterparts. And certainly, amps that use an octet (of more) or KT88 (or whatever) really rack up the tube bill! I just swapped an octet of Tung-Sol KT120 in place of Gold Lion KT88 for a VAC statement 450S. Made a HUGE difference. I also swapped its sextet of 6SN7’s (mix of NOS and new). That made a smaller (but still large) difference - and yes I tried many various combinations! In other amps I have preferred Gold Lion KT88 over KT120. And EH KT88 also sound different from GL KT88, despite being made in the same factory - just a matter or personal preference (GL are voiced more "audiophile").

The KT88 and KT120 are close enough to be reasonably compatible (bias, loading etc), but different enough to sound quite different. It’s a fun swap :)
Just clear it with your amp maker first. Anything running a KT120 near its limits would fry a KT88, and KT120 draw a bit more heater current from the power transformer.

As for JJ - I had a run of bad JJ encounters in the past (~15 years ago) and never gave them another chance since then. My rule for the longest time has been to bin JJs immediately, whenever a component arrives with them inside. 

all of the above but try the small tubes first, you may find you tune the sound to your liking without expensive power tube trial and error experimentation.

jj tubes are like $40 apiece and the cheapest versus others in the $80 to 150 range

I’m looking for a cleaner Open sound. There are for preamp tubes and it seems this tube is the beginning which sets the stage for the signal and then the power tubes. So I guess starting at the beginning of the food chain makes more sense.

Although I do hear that the JJ tubes are more durable and reliable which is why I guess they use them as stock tubes.

What kind of amps are you running? 16 power tubes? WAG, but sounds like some Primalunas I've seen, but not heard. What kind of 'signal' tubes are you running? What kind of pre-amp are you running, with what kind of 'signal tubes?

Specificity might get you a better quality of response.