Breakdown of Turntable Performance

Ideally it should be:
Cartridge 100%
Arm, Platter and Plinth 0%

With the very best tables and arms I would say:
Cartridge 90%
Arm 4%
Platter 1%
Plinth 1%
Outside influences 4%

With a typical mid Fi table:
Cartridge 70%
Arm 10%
Platter 4%
Plinth 12%
Outside influences 4%

For what it's worth, I recently had a $385 cartridge sound much better than a $1200  one that I have. With the turntables I have had, the arm and platter bearing made the biggest differences. YMMV.

Everything is built on a foundation. If anything below the seperate stages of each individual stage is comprimised then EVERYTHING above it is multiplied increasingly.
Self noise from motors not mentioned here in my experience do far more harm.
Its a weakest link scenario regardless of personal bias . Cause and effect...they all matter equally in the bigger picture...

I'd start with a tt's ability to have it's platter effectivly isolated from its bearing.

A $50 AT95E cartridge on my Music Hall MMF 7.1 sounded better than a $800 Clearaudio Virtuoso Wood on my Music Hall MMF 2.2 table.  Better feet, a more solid plinth, a detached motor, a better tonearm, better wiring... those things all matter. 

Where it especially makes a difference is in the bass, but also throughout the entire range.  No matter what mods I've made to the 2.2 or what cartridge I put on it, the bass has that "cardboard" sound (I don't know a better way to describe it) while it is very solid and tight on the 7.1.  The cheaper turntable just doesn't have the same level of vibration isolation and it's apparent in the sound.

A cartridge can perhaps have more impact on the character of the turntable's sound much like speakers do, but much like your entire system, if you have a sub-par source, amp, and/or preamp ahead of the speakers, they may sound different, but not as good as lesser speakers would with better electronics in front of them.  

If I had a $1000 budget I'd rather have a $700 table with a $300 cartridge than a $300 table with a $700 cartridge.