Turntable versus tonearm versus cartridge: which is MOST important?

Perhaps it is not as extreme as this hypothetical, but, I know someone who bought a $5,000 cartridge to temporarily use on the cheapest Pro-ject table.  I helped another friend with the installation, which included milling a heavier counterweight to use than the one supplied by Pro-ject.  The installation involved using a Feickert protractor, and a very good digital scale (I own equipment for setting azimuth electronically, but, we thought this is overkill for this installation). The combination sounded good, except for some noticeable inner groove distortion.  The distortion was probably from the arm being barely able to handle the vibrational energy from the cartridge.  When the cartridge was installed in its permanent home, an EMT turntable/arm, there were no issues with inner groove distortion.

In my humble experience (40 years) your hunch would be incorrect. A proper turntable and tonearm (more expensive) will allow you to extract the most performance from a $500.00 phono cartridge. You will then have a platform (turntable/tonearm) that will reveal further improvements in phono cartridge performance down the road.

Summed up or put another way; buy the very best turntable and tonearm you can afford FIRST.

This can be stated simply and is easily and repeatably demonstrated. The ability of the arm to track the cartridge correctly is far more important than which cartridge you have. Put another way, if the arm can't track the cartridge you won't be able to fix it with the most expensive or 'best' tracking cartridge made.

The cartridge!

atmasphere 

Well said.