What is the order of importance of the parts of an analogue rig?

@sokogear : "  What about SUTs (set up transformers). Should that be a separate category for those with MC cartridges? "

it depends on the Phono stage design. Some designs has not enough gain and the designer opted by a passive gain stage through an internal SUT other designers opted by active high gain stage that does not needs a SUT and the stand alone SUT normally is used with Phono stages that handled only MM cartridges.

Even there are gentlemans that own an active high gain Phono stage and listen their LOMC cartridges through an stand alone SUT and this means that the cartridge signal will be added with several kind of developed distortions ( every kind of. ) for the use of additional IC cables between the Phono stage and the external SUT. 
Now the cartridge signal must travel for a half cable or 1m. cable that degrades the signal an exposes the signal to RFI, EMI, external vibrations, etc, etc. and not only that but the cartridge signal must pass through additional RCA/XLR input connectors and solder points adding more degradation and what happens at the Phono stage input connectors is duplicated at the SUT output connectors too. Along all those the cartridge signal must pass several meters of wire in the SUT internal transformers.

That's why : ""   that were trans-formative to the performance. ""

As an active high gain stage the passive SUT/stage can be addictive but certainly different.

R.

Dear friends: In an analogue rig and " everything the same " scenario/premise what can makes differences for the better or worst are each one commited to overall choosed analog rigs and  set up details.

Everything matters down there, @mikelavigne  already posted,  additional for me the first importance belongs to the cartridge self tracking abilities along its well matched tonearm because what we want is that the cartridge can pick-up as many recorded information as it can and to achieve that its tracking abilities can make a paramount differences if your room/system has a good overall resolution.
Now for that cartridge abilities can be showed the cartridge/Tonearm/TT must be douing in an accurated way: this is a must to have.

Down the cartridge/tonearm is very important the tonearm internal wiring quality and if the tonearm is a removable headshell design then the headshell connection wires and that the headshell will be matched to that cartridge.

The evil/enemies of the analog rig are the developed distortions /(everykind: noises, vibrations, resonances, EMI/RF, etc, etc. ) generated by the analog rig and the room. Important link in the analog rig where the TT is " seated " to avoid the develops of distotions.

So with have to find out ( in our system ) first those distortions, second from where are developed and third how to put all at minimum and for all these we need first hand experiences coming from every where and to have a evaluation bullet proof whole process.

Mats, clamps, cables makes a difference and if we have not the knowledge level and skills we can't really be aware if changing the TT mat for other one really makes a difference for the better or only a different sound but not better sound.

Fine tunning the analog rig is the name of the game down there and this means time and patience to achieve it: years not weeks.

After all those the choice of Phonolinepreamp is of critical importance because the cartridge information that always will be losted in that device we never have the chance to recovery, so the Phonolinepreamp is of vital importance because inside it are developed perhaps the higher distortions ( every kind of. ) in the analog rig.

Regards and enjot the MUSIC NOT DISTORTIONS,
R.