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. 

Millercarbon said it all.
My addendum:The most economical route may be to keep on upgrading arm and table, while having a cheap(er) cartridge that can step up big way.Not all cartridges can step up when the table/arm combo is greatly elevated.I found the Audiotechnica ATF7 is such a hidden gem. Totally inexpensive LOMC cartridge, as cheap as LOMC can get. I got it as a backup cartridge to test play my second hand records. On the big table it plays in big cartridge league, and each improvement on arm / table / step up made it step up higher and higher. Athough, I have to add I never tried it on the Rega or other cheaper tables / arms, so don't know how it performs on a cheap table... but that's kind of out of the question as LOMC step up on the cheap is pretty bad. In the low price range MM is the way to go. A cheap MM cartridge that can play big time on big tables is the AT440MLa or MLb. (good luck finding MLa version! But sadly even the AT440MLb have become quite expensive now, while 20 years ago it was a cheap(ish) cartridge!) On a basic table (Rega P3, with Rega arm) for example the AT440MLb and the Grado Prestige sound quite in the same league - different presentation style, but similar performance. Put them on a big VPI-caliber table, and the AT440MLb skyrockets and the little Grado falls apart. The ATF7 is cheaper than the AT440MLb, yet on a big table it completely eclipses the AT440MLb. Yet, the AT440MLb has nothing to be ashamed of either, and its lifespan and durability is absolutely outstanding.

Dear  @mijostyn : "  the rest of us are hallucinatory. ", not exactly.

I think that problem is that several of the posts are taking the TT and tonearm main characteristics to make a good job, are " disecting " each item when in my view it's an issue that should ve analised as a whole one.

Yes, if the TT has not a decent speed stability then we have to fix it changing it but with that kind of " attitude " it's " healthy " to say that the more important link is the electrical power or the TT arm mount or its type of screws used on it and all these is " crazy " for say the least. There is no whole context is almost " stupid ".

For me the issue is not to analyse each item link isolated but as a whole system with specific premises.

All we know the importance of TT speed stability and about non-vibrational plynths or about the rigth TT mat and clamp: so what? all those each item characteristics are implicit when we are talking of TT. We are not newcomers, do you?

As I said we need an overall context with scaled analog system . For me has no sense try to do it as other gentlemans already did it.

Obviously makes sense to you and to them.

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

Which is more important: speakers or an amp?

Transducers are the ones that have the higher posibilities to make higher differences for the better or for worst.

Analog is simple but really complex due to its imperfections levels everywhere down there with to many different " parameters " with an inherent relationship in between. It's a madness and you said that TT/tonearm comes first?

Everything is important and that's why we should try to talk on not isolated items scenario but as a scaled systems.

Good for you and the other gentlemans that are happy inside that " hallucinatory " mind scenario. Go a head ! ! ! 

R.

Raul, no sensible audiophile could disagree with what you wrote. (Is the term “sensible audiophile” an oxymoron?) But at the outset, the OP wrote that he did not want responses to the effect that everything is important. This I think drove the tenor of the responses he’s gotten. I dislike such questions per se, but I was bored enough at that moment to concoct a response. With an excellent TT and tonearm, you can get a lot of juice out of a mediocre cartridge, but I don’t think the reverse is true. Not in my experience.

@chakster
"I’ll tell you more: change the stylus tip on your cartridge and you will change the whole sound."
I agree completely. I just re-tipped the Zyx Omega G cartridge and the sound is completely different with the original. Better or worse is another story.