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

WOW. I wasn't thinking about that high a level of commitment. At my level, I was amazed at how much the sound improved with an upgraded arm (REGA RB 700 to RB 880). Then I moved the turntable from a P5 to a P8 and it was subtly better, but was not blown away to the same degree, but I like a couple features it has. I learned late in life how the Phono stage is so important (much more so with a MC cartridge). When I got one that matched the impedence of my cartridge (which was and still is the best part of the system) I couldn't believe it over the one included on a very nice integrated amp (although with the kind of $$ you are talking about you'd never consider that).

The point of the question is theoretical in nature...what part of a rig could improving be most beneficial? I realize that is never true. The Linn mindset was always engineering focused at to the source of the sound, so cartridge came first, but I agree if there is excessive motor noise (or the record stinks) it is a moot point.

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.

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

Everything is important and contributes to the overall sound.

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

with 2 of my 3 turntables i have recently added EMIA Silver wound 1:10 SUT's that were trans-formative to the performance.

http://www.myemia.com/SUT.html