What is the chain of importance in analog system ?

Well, the answers will be always different, because everyone has made his own experiences. Let's say, everyone of us started with a budget System, quite nice and the "upgrade" started. Upgrade means, more money--> better result.
After a while everyone thinks (not everyone, but most), "hey, I invested money, I got better results, so the good units have to be expensive...."
(or some think about ---> what's the background...why? What's the ability from the unit and what it can/should do (better..)
or others rely on the "opinion" of the "Competent" (writers, Designers, friends etc.)

But when these are all so clever, why there still are so huge differences in Playback?
Let's think about:
Phonostage
This very small signal has to be amplified, high gain, no distortion, Soundstage, depth, Body etc., the Illusion of being there has to be created..
Can everyone do that?
No, this is really difficult, only a few have superior knowledge, the main reason why there are so many average Phonostages are out there. Price is no guarantee for top quality. I use a Vendetta, made 1990 and this one is better than everything I listened to( true tone, depth, soundstage, speed, focus, Image...) in the past 10 years.
Turntable
Difficult to make? No. There are endless units available...
Everyone does it, parts are Standard, most invest everything they have in the Look and weight. "This is the sign for a real serious machine" :-)
Some Marketing, some Hype, good profit for Dealers and it is done.
How about suspension? Internal, External? Bearing quality? Different materials in the Platter? Damped Armboards?
Simple answer: Too complicated, too expensive, no Knowledge. the main reason why most TT's are more or less at the same level , 3000$ or 30000S
Arm
any Designs out there which outperform AT ONCE a Fr-64s/FR-66s or a Phantom (the only obe which is clever continued in its design)?
Piece of wood on strings for 7k? or a piece made from Kevlar?....
Easy choice, good Arms are available for 2k used
Cartridge
What is the difference between 2000$ and 8000$
ok, no war, but here you can really burn money.
The Designer has the same time to make it, he can waste his time with cheap ones or with better ones (which are normally only better in selection)
or
you buy a stone body, here there works needs a little bit longer...

Arm cable
has to be shielded and should be able to carry low level signals without damping or distortion.
Available for 400$ and for 4000$
for those who think that the only way to High End is High Income :-)

Now,
what works?
Expensive, but inferior Phonostage with a expensive but average Design multi Motor Turntable and a 8k cartridge which will be thrown away when the owner sends it back for "rebuild"
or
expensive, but really clever made Phonostage with a regular priced clever made Turntable (4k) and a regular, but good designed Tonearm (1.5k) and a second hand cartridge for 1.5k)

I vote for the last
IMHO :-)

Given that some arms do not work on some tables due to mechanical incompatibility, you can make an argument that you have to look at a complete "record player" as a system. And the same argument is true on the electronics side; some phono stages do not work well with some carts due to electrical incompatibility and some phono stages will not work well w some line stages due to inadequate gain or other issues. So I think you have to assume that all elements has been chosen for compatibility, both electrical and mechanical, and that all items are of more or less equal "quality" (whatever that means). In other words, an upgrade path or resource allocation type model. Then I would say that phono stage is most important, and then the cart. The phono stage for all the reasons noted above. The cart because in my experience, transducers, whether we are talking mechanical to electrical (cart), electrical to mechanical (speaker) and even electrical to visual (video display), have a very significant impact on overall character of a system. As Dopogue said:

"I've heard cheap carts sound amazing on great platforms, but I've never heard a high-priced cart sound good on a cheap platform." . I would just replace cheap with inexpensive.

An argument can also be made that given a good transducer that has no major sins of "commission" (not colored, well balanced throughout its operating range), then good electronics is key. This is akin to the average speakers with very high resolution/excellent electronics will sound better than average electronics with very high resolution/excellent speakers.

Put this all together, and I would opt for an excellent, high resolution phono stage, a good, well balanced/neutral cartridge, a good speed stable turntable and a very good tone arm. In order of expenditure (in relative $, relative to what a middle of road unit of that particular type would cost) I would prioritize as follows:
1. Phono stage
2. Tone arm
3. Cartridge
4. Table

Of course if you are VERY susceptible to pitch variation, and/or consider pitch accuracy critical to your enjoyment, then the table and more specifically the motor and speed controller may be elevated in the hierarchy.

An aside to Dopogue/Dave- Not surprised at your comment about the Rhea vs the NYAL Super-IT. At that price ($4k), my experience in head to head comparisons (with several other listeners all agreeing) is that you can do much better than the Rhea, either in standard or SE/NOS dress. For example, the ZYX Artisan, which is a great value right now if Sorasound still has any close-out units, or a used Manley Steelhead would be two very good choices. Also the phono stage in the VAC Ren Mk 2 beat the Rhea, if you would consider changing to a full function pre. I really wanted to like the Rhea due to its flexibility and ergonomics, but unfortunately I was not impressed. Table/cart/arm for all comparisons was Teres 3XX, Tri-p MK VII, ZYX Uni.

Those that say every item in the chain is important are right. There's no possible discussion beyond that correct answer. Now, if I were trying to put together that system I'd listen for musical balance with items inserted into the system and get the best items to match to musical presentation I want.

Now if starting from an entry or mid-level point and if I knew I was going to upgrade further later I'd base the chain with best phone stage I can afford. What follows IMHO is balanced on performance available/costs:

Your great Phono Stage
1. Turntable
2. Arm
3. Cartridge
4. Arm cable

enjoy the music first - every thing beyond that is ego

Dear friens: I would like to add something on the subject.

What is what we have on the market/commercialy in each analog audio link? which is its overall quality performance? how that real quality performance affect the cartridge signal reproduction?

These are my experiences on the whole subject through the last 3-4 years and what I think about:

if we take the TT analog audio link and if we separate by at least one characteristic like the suspension type and two-three price ranges we can assess that the quality performance differences of each TT in its price range/characteristic are minimal and makes ( everything the same ) small differences on the cartridge signal quality sound reproduction.

if we take tonearms and separate for at least one characteristic like pivoted and linear tracking and two-three price ranges we can assess that each tonearm in its price range place has almost the same quality but when we mount the cartridge then the quality cartridge signal sound reproduction change not in tiny proportion but with big differences that many times does not have any relationship with the price each tonearm range place/position.
Almost everyone one of us can assess this when we change the cartridge to other tonearm and souns better and many times we say: " Hey this tonearm is better ", when what is better is not the tonearm by it self but a better cartridge/tonearm match, that's all.

if we take phono stages we have to take at least one characteristic: stand alone and integrated ( phono stage + line stage. ) with 2-3 price ranges too.
Here is where IMHO we have more or in high grade quality performance differences ( as always everything the same. ) in each price range due to an average/mediocre designs and differences between those designs.
Gregm posted: +++++ " BUT, few of us really have a good phono..... " +++++

and I agree because there are only a few first rate designs that along our not in deep know how about makes that the Phono Stage is the weak link in almost any of the analog audio chain in our audio systems.
I hope that in a near future the phono stage link can lower ( by a wide margin ) its differences for the better.

if we take cartridges the " stage " is similar to the tonearm one and only when we match in perfect way the cartridge with the right tonearm we can really heard the cartridge real quality performance ( everything the same. ) and its real differences.

As almost everyone posted: each link is important and no doubt about but for me and due to its today real contribution I have to stay with: Phono stage, tonearm/cartridge and TT in that order. Things can change over the time or system by system due to our overall knowledge on music/sound reproduction and our own priorities.

Regards and enjoy the music,
Raul.

Swampwalker, I clearly shortchanged my former phonostage. Yes, there was a "SuperIt" (itself modded) at the center of a large box -- as large as the Rhea --fed by a tubed power supply the size of a power amp. So beating it is not a casual feat, and the Rhea is not going anywhere soon. Especially after the last rounds of tube- and cable-rolling (balanced HMS Gran Finale between Rhea and Calypso).

Cheap= inexpensive in my book. Sorry about that :-)