Turntable versus tonearm versus cartridge: which is MOST important?

Put a Reed 3P arm on any of George Merrill's Gem Dandy polytables and mount the bargain cartridge of your choice and you can get utterly amazing sound. 
Another similar scenario is put any of the arms offered by Pure Fidelity (my choice would be the Acoustic Signature TA-2000) https://purefidelity.ca/turntables.html along with one of their tables and any reasonably good budget cartridge and again, amazing sound. 
For me, against all of my expectations years ago, it is tonearm first, table second, and cartridge last. 
When it comes to the drive system, speed control, motor noise isolation and Fremer's finger tap test are all aspects of vinyl playing that appeal to measurement nerds but in real life take a second chair to sound reliability/durability with decent but not all-out design principles. 
The turntable needs to be good, not stellar. The tonearm needs to be stellar. There a huge bargains in current cartridge offerings. 

Never mind , transducers always are the most important links in any audio system.

Raul, anyone who has ever spent ten seconds on this Board in the last ten years knows you have a unrequited out of control cartridge fetish. I envision you sleeping on a mattress surrounded by cartridge boxes. 

Transducers are not the most important part of the audio system. You may believe so and you have every right to your belief but many argue otherwise, and I am among the latter camp. Look up Herb Reichert's recent tale of wandering into an audio store and being introduced to Naim gear set up with inexpensive loudspeakers for a good anecdotal account of the opposing view. 
Cartridges and loudspeakers are very simple devices. Only audiophiles make them out to be more complicated and exotic than they really are. Do they have the biggest influence on sound character? That is a different question. Sorta like are noses the most dominant feature on a face? Yeah, most times and certainly on mine! That does not make them the most critical component. 
Feed a pair of the most expensive loudspeaker on the planet (any of the top 50) with a mediocre amplifier and preamplifier and you can never get anything better than mediocre to good sound. Pair a pedestrian set of loudspeakers (critically positioned in the room they are in) up with a stellar amp and pre-amp and you can get great sound. 
Which brings us back to the current debate which has surfaced time and time again. Like my nose joke, turntables get the most attention because-imho-they are the most prominent item. The choice of drive unit is almost inevitably made first. It draws all the attention of would-be buyers. Ooooh, look at that huge platter! Ooooh, look at that outboard power supply with a digital read out! You get the idea. Most of us are guilty of that misdirected (again, must my humble op) focus. 
I am biased perhaps because I got off the modern era table bandwagon and went to vintage with Reed 3P arms though I have spent considerable money on cartridges. But I know that could give up those cartridges and mount a $250 Audio Technica or Denon and get fantastic sound. 

After many years of using various tonearms including four different VPI arms, the 3D printed plastic arm included, I installed my first Reed 3P. It was an epiphanous moment. The huge sonic difference is no doubt due to the amazingly talented designer Vidmantas Triukas. The experience convinced me that if I had to choose between a $250,000 Tech Das table mated to lets say a VPI arm, which I believe to he kludged together pieces of junk, or a restored Garrard 301 with a Reed 3P, I would choose the latter every day of the week and Sunday too. It-the discovery and conclusion-was against all of my pre-conceived notions and assumptions. Enlightenment. May it come to you too. I am self-aware that this sounds arrogant on my part. But once you hear a really well designed arm there is no going back. 

I have a 12" Cocobolo with Firewire and a 10.5" Ebony with Firewire. 
My 12" is paired up with my heavily modded TD124 and my 10.5 is on my modded 301. You can see pics in my profile 

I won't waste bandwidth by quoting Ralph's post of today at 3:35 pm but it echoes what I have been trying to say in this thread. Take a well designed no frills drive like a Gem Dandy or PureFidelity (among any number of other candidates), fit it with a great arm and a $100-$250 cartridge, get it dialed in and watch the awe and amazement ensue. You CAN NOT replicate the same result with either of the other two possible combinations. And yes, there are theoretically nine total combinations so you can look at this way too-any combination that does not include an excellent tonearm is doomed.