Turntable versus tonearm versus cartridge: which is MOST important?

The Cartridge>Tonearm>TT or however the configuration of the items is assembled are in my mind not able to one item set aside as having the most importance. In terms of replaying a Vinyl LP it is this trinity configuration that proves to be the most successful method.
Each item is this trinity are totally dependent on each other and each item success within this trinity is dependent on critical tolerances for the designs of mechanics and critical dimensions for the geometric interface between the items in this trinity.
All parts will need to interface within the very well known geometric parameters and each part will need to function to the accurate designed mechanical operation.
If a item can not interface within the trinity that caters for the meeting the critical mechanical function and geometric interface, then in my mind it is only then that the item will fall from being of importance within the assembly.
There are Various Brands, Various Purchase Values and Numerous Ancillaries on offer of Items to produce the trinity.
If the designs from these producers are capable to achieve the above then the ideal set up can be achieved at a variety of budgets.          

Normally one would expect the cartridge to be the most important.  After all it is a transducer - the others being microphones and loudspeakers.

However it is the turntable that is the most important.  First, there are speed issues.  This is expensive to get right.  The cost effective way is to get a Direct Drive.  Second is vibrations.  This is critical because the signal from a cartridge is magnified some 10,000 times form cartridge to loudspeaker.  So the smallest imperfections are audible.  Vibrations come from ambient vibrations in the room (typically from outside the room), footfall, the cartridge itself colliding with the vinyl wall (and often magnified by the platter), the sound from the speakers themselves hitting the turntable, the bearing.  All these issues can be resolved but not easily.  

Compare this to a tonearm.  They have their issues but the difference between an average tonearm and a top one is not as much as any other Analogue component, even including phono stages.  I bought a very high end tonearm from Origin Live, but with a few months I sold it and went back to my Jelco.

My ranking from most to least:
Turntable;
Cartridge;
Phono Stage;
Tonearm.

@fsonicsmith , could not have said it better. 1+

The question should be, "how do you go about building a great turntable?"  That fact is you have to evaluate each item, drive, tonearm and cartridge individually then determine if they function together. Obviously you have to stay within your budget. The order is Turntable then tonearm then cartridge. It is no good to pick a tonearm that will not fit on a turntable you can afford. The turntable is generally the most expensive part of the deal so you start there then pick a tonearm that will fit and finally pick a cartridge that is matched to that arm. Since the cartridge is last if you have to skimp this is were you do it. Cartridges are also wear items. If you can't handle this then you can buy a stand alone unit like a Thorens, Rega, Project, Music Hall and so forth. 

Wow this question has caused a few sparks!!

And some varied responses, all the better to understand the issue.

Basically, I'm in the process of upgrading my TT in my second system.  The current unit is vintage (Pioneer PL600 - the good one) into a Hana EL cartridge.  Total investment: $500.

Had the opportunity to directly compare it in my system to a Clearaudio Performance DC/Satisfy Carbon arm/Lyra Delos cartridge.  Total cost around $7K.

The latter was better in most parameters especially with respect to dynamics, detail, resolution.  Tonality/frequency balance was more natural with the vintage system (less upper frequency glare).  Bass was comparable between each unit.  Both rigs were enjoyable to listen to.

So naturally I'm trying to determine how much of the sonic differences are due to the cartridges themselves, versus the other components.  Ideally I'd like the resolution of the new rig and the tonal balance of the vintage set up.

The system: EAT Petit phono, Classe DR5 line stage, Pass XA25 amplifier, Joseph Audio Pulsar 2's on Sound Anchors.

So there you have it ...