What is the chain of importance in analog system ?

I think the phono stage is the most important because without it you can't play a record(sarcasim).This is like saying the record is the most important. Yes, the vinyl is the reason for the playback system but isn't that stating the obvious? And puting a playback system together is alot like puting a ball team together like, let's say the Yankees. Just because you have the highest payroll or the best player at a position doesn't mean you'll have the best performing team (maybe this analogy isn't quite right considering NY's success this year). Jaybo is right, your expectations should be realistic. The turntable is responsible for bass extension, the rhythm and pace, and what makes analog sound better than digital. It affects the ultimate S/N ratio either adding noise or getting out of the way and letting the arm/cart do its thing. Belt drive is the way to go. Try reading some of the old Linn Lit. It makes sense.
http://www.linn.co.uk/music_systems_sondek_LP12

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 :-)