I found each tube makes some difference. If I list in order of priority:
1. 12au7. Sets the overall character. I have several (RCA, Mullard, Tung-sol, CBS, 5814's, etc). My preference is CBS (either 12au7 or 5814) in my system and for my ears. Some have a little more low end and some a little more sparkle (high end).
2. 12ax7 initial position (first stage of amplification).
3. Rectifier
4. Second 12ax7.
I prefer the LPS over the JJ ax7, but both are fine. My preference is RCA
or Amperex, which I picked up used. Tried a Telefunken, but didn't like it as much.
With 4 tubes, there are dozens of mix and match options.
Recommended accessory - tube dampers. They change the sound. Tighten everything up, remove glare or distortion, and enhance the feeling of a deeper low end. You lose some "air", but you also can just use a damper on 1 or 2 tubes. First 12ax7 is most sensitive to dampers.
Rather than spend a ton of money on NOS, see if you have a ham fest swap meet in your area and see if you can scrounge some used tubes there. That's where I picked up most of my tubes.