Fine tuning the system. Where do you start and how do you proceed ?

Start by assessing what you like about the sound you are getting and what improvements you want.  Keep in mind that anything that you do, if it is at all effective, alters the sound and that can be for better or worse.  Be prepared to accept that something you do might have to undone.  I am amazed at how many threads talking about power cords, interconnects and tweaks have very little comment about changes that were detrimental when there should be a lot more instances where a change in sound went the wrong way.  It helps to be more open minded about one’s own purchases.  
 

With tube gear, I would start with trying different tubes based on commonly shared experiences reported about tubes.  Some tubes are warmer sounding, or more dynamic and detailed sounding, etc.  I would start with the cheaper tubes, which tend to small signal input and driver tubes.  Even though they can be much more expensive, consider vintage tubes—many are much better than current production.

Interconnects and speaker cables would be next for me; they tend to make a bigger difference than power cords.  But, if you are using the cords that came with the gear, junk that and go with something a little better before searching for the ultimate set of power cords.  You will hear differences between very good chords, but that difference is comparatively subtle and more evident when you have dialed in the rest of your system.

Vibration damping/control via specialized racks, equipment footers, etc. can have substantial impact on sound and I personally find it is easy to overdo this and end up going the wrong way.  Sometimes you don’t even know you goofed until you pull all the stuff out and find out that you now like your system more.

I roll tubes I've rolled cables a little bit of isolation and things sound pretty good here. It's really about trying things and then living with them. Don't jump to immediate conclusions I usually take at least a month to get my head around changes and it becomes more of a vibe thing can I relax into the music or not.

First, the room makes by far the most significant contribution to sound quality (with exception of near field and headphone listening). so discounting room is the a first order mistake.

Second, I listen to music not test records. A good system makes an average record sound good. There is much more variation amongst recordings than there is between system tweaks. So I don't sweat it too much, listen to more music.

I got Paul McGowan's book and test CD. The problem is that the bass test track is played horribly out of tune, so just painful to listen to. And then the phase track did not do anything only to learn that it does not matter in many situations/to many listeners. Total waste of money and time. I learned my lesson and ignore test tracks.

The room, setup, and placement are huge factors. Assuming the gear is good, and cables aren’t the weak link, speaker placement is typically low hanging fruit. I tend to use the music I listen to most as my reference, at least the ones that are decent recordings. Some recordings have more bass, some less, so it’s good to find a happy medium with the stuff you listen to most often.

Isolation of your gear is another subtle way to optimize things, and squeeze a bit more refinement....TT, amps/pre, speakers. TT and preamp are on sorbothane feet. speakers are on isolation spring pucks, amps are on rubber/cork feet.

I tend to use tube rolling and cable changes for final tweaks to dial in the sound I want. There are really no hard fast rules....it’s very subjective, and very unique to your setup, so you have to experiment a bit.

Once I was pretty happy with the overall balance, presentation, and synergy is about the time I started upgrading power supplies and opamps in my DAC and phono stage for a bit more refinement.  Wall warts got replaced with linear regulated power supplies.

Do it step by step, one at a time - that's an excellent advice.

Looking for best pressings is an almost never ending process, but before that you have to find out what the best pressings are. Sometimes it's difficult to know before actually comparing. But this can make very big differences.

My turntable is on a thick maple block which in turn is on the floor. There are big Boston Audio graphite tune blocks under the maple platform. Seems to work fine. Integrated tube amp is also on a thick maple block which is on the floor with Audiopoints brass cones under it. Two tape decks and PS Audio regenerator are on the rack. The Salamander rack is no good but since both the turntable and amp are on the floor, I see no reason to replace it.

Tubes in the amp are excellent, all NOS Mullards and RCAs. I do have to replace tubes for the phono, probably with Mullards or RCAs but might try Raytheon black plates.

Cables are more than adequate, and Nottingham Spacearm's cable goes from the cartridge right into the onboard phono stage amp, no need for separate tonearm cable or interconnects. The table has Boston Audio graphite mat instead of stock.

So, I am not sure what I might want to do in terms of fine tuning. Perhaps some feet under the amp.

Speakers are placed as well as they could be in the room, and most of the listening is close to near field listening.