Turntable versus tonearm versus cartridge: which is MOST important?

I would suggest to you that in an analog audio system the most crucial is where the translations occur. The cartridge translates the record groove into an electrical signal and the speaker translates the electrical signal into the wiggling air molecules that we hear as sound. But just as the performance of the speaker depends on the interaction with the listening room, so does the performance of the cartridge depend on the interaction with tonearm and turntable. They are the 'environments' in which the transducers need to operate, so in a sense the turntable/tonearm is the cartridge's room.
If these environments are not capable of eliminating the most intrusive audible  interferences (noisy bearings and motor instability with tonearm/turntable platform, standing waves and other acoustic anomalies in a room, etc.) these transducers will never reach their full potential.

So a high quality turntable/tonearm platform that largely eliminates these intrusions is where you should start, but in today's niche market this usually costs big money. But if you're prepared to look back in time you will discover that most of these problems were already dealt with pretty succesfully in the 20th century, when analog playback was still the dominant music playback source. No need to spend 10k, as $1500 for a solid 80's turntable and another $1500 for a really good vintage tonearm will provide you with the largely non intrusive platform that is required to take full benefit of the best cartridges. This is when tonearm/cartridge synergy will start to make sense and you will discover that certain combinations will sing beyond your wildest expectations, to a certain extend even regardless of the cartridge cost. This is where the fun really begins.

However, be aware that such a quality platform will not magically make a budget cartridge sound like a top level one. I know there are people who believe a Denon DL103 is all they need, but you know what they say about polishing a turd.....

$10K cartridge and $500 turntable/arm is a total nonsense, but 10K turntable/arm and $500 cartridge is not too much of nonsense. I can imagine people using Denon D103r or AT150mlx (about $500 MC and MM cartridges) on their 10K turntable/arm. So, the latter approach makes much more sense.
Probably $10K turntable/arm and $50 cartridge is as much nonsense as the former.  
Having said that, IMHO, getting near perfect match of turntable, arm, cartridge, and plinth is extremely hard for novices (myself included) if purchased separately. If you are a DIY type of person, it will be fun to play around, but it will still take lots of time/money/effort to make it right.

in my opinion
most important tonearm more than the cart. especially the case for MC

TT is quite subjective... can works both way. also depending on the type of plinth. isolation. type of drive. so don't really have an opinion. 

I think we have safely established that the turntable/tonearm are more important than the cartridge for starters, a rare moment of almost total agreement. 

@mijostyn,
A rare moment of almost total agreement indeed. Especially considering the various vested interests at play. A few cartridge vendors may be heard mumbling at the back, but mostly everyone else is in accord.

I'd also add that the turntable is more important than the arm because it provides a resonance free platform for the arm/cartridge combination to do their work.

The turntable also needs accuracy of playback speed and hence pitch.
That's why rumble and wow and flutter measurements are held to be so important.
Anyway here's an opinion from someone who should know.



"Turntable differences are greater than any other item of Hi Fi equipment.

CD players sound different to one another, but not a lot in comparison to turntables.

-----

A better turntable will improve the clarity, dynamics and ability to follow every strand of the music plus other aspects too numerous to mention. Gone is blurred, woolly bass and general confusion in the sound."

"No matter how good your cartridge is, it’s been proved that it can never perform at anything like it’s true capability without a good tonearm.

In the same way, a relatively inexpensive cartridge worth £50 can outperform one that costs £1250 simply by being installed on a better arm."

These are the words of respected tonearm makers Origin Live - even if the price /performance ratio isn't always a linear one.

Something which Origin Live themselves demonstrated some while back.

https://www.originlive.com/