What is the chain of importance in analog system ?

I personally don't feel any part of the chain is more important than the other. Imagine our audio chain being a bunch of filters all lined up in a row. Depending on the filter positioning will determine what will get through. The LP is the liquid. If you have a filter different than the others at any point of the chain then you will be hearing the filter. This of course includes speakers. IMO speakers can be more important than anything. If you source (in this case analogue front end) is better than your speakers can resolve, it truly won't matter. And getting to Kr4s point of room, I would add room/speaker as a single unit. I would match a system that has complimentary equipment based on what you have heard. That is unless you plan on upgrading in the future, then match a system at a higher level, and buy th part you can afford and then upgrade other areas as it permits. But getting a great phono stage without a well matched cartridge only gives you a great phono stage. The cartridge will still only be as good as the arm / turntable etc. So make a decision to be close to equal. Now in terms of money, a lot will depend on the type of cartridge or sound you prefer that will determine appropriate matching equipment.

I think one also needs to look at the upgrade path as well as sonic order of merit. Having an great table or arm to be the foundation for even a modest cartridge will yield excellent results. While I was waiting for my Strain Gauge cart to be delivered (I'm a dealer) , I used one of Soundsmith's $300 MM carts on my Raven One/Phantom.

I was shocked at how good the cart sounded. So perhaps the cart should be modest at first, since it can be upgraded later as more money allows, and you always have the modest cart as a backup.

...some analog guru said, that the most important is the phono stage, then the table, arm, cart

I the grand scheme of things I would agree with the guru.
BUT, few of us really have a good phono (we may think we do, but try a Boulder or a FM Acoustics on yr system...) which are invariably (ridiculously) expensive.
Furthermore few of us achieve the right loading.

SO, I join our friend above in putting "deep pockets" at top position.
Then comes phono, TT, arm, etc. Don;t forget the X?@! wire!

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.