Breakdown of Turntable Performance

Some would say pretty much the exact opposite.  Platter/plinth most important, arm second, cartridge last.  Depends on who you ask I guess. 
But when you think about it - the plinth and platter need to be designed to be immune to feedback and turn the record at the proper speed.  The arm must be designed so as to extract the maximum info from the cartridge.  Many feel a better arm and cheaper cart work better than the opposite.

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.