What is the chain of importance in analog system ?

Raul's experience mirrors my own, with one minor exception.
(I put the tone arm cabling with the importance of the tone arm, rather than with the turntable. I've heard some mediocre cabling on an otherwise decent tone arm, and after upgrading it, the performance was elevated tremendously.)

But of course, as it always is with assembling an audio system, the weakest link in your audio chain will always be the limiting factor. All of these items are very important, and upgrading one well beyond the others will yield limited benefits. So my chain of importance would be as follows:

1a. Phono Stage (and especially so with LOMC cartridges)
1b. Tone arm, (including cabling) and Cartridge
1c. Turntable

(Notice that they are all number 1 in importance, with just subtle subcategories! :-)

My two cents worth anyway.

There is no single chain of importance that you can follow alone to assure good results.

IF the gear is decent and you set it up correctly and each part integrates well, it will sound good. Otherwise it will not.

Once you set up any decent gear correctly, changing cartridge and/or phono stage will make the biggest difference in the resulting sound.

I think the turntable is the most important componet in an 'analoge chain' and this is where one should start. The success of a record playback system depends more on its mechanical interfaces/synergy than on its electrical componet. If I had to make an order of effect it would go like this:
1) turntable
2) tonearm
3) cartridge
4) phono
Cartridge/arm matching is important as is cart mounting, alignment and tracking angle.
That being said I would pick my table first,then cart,and pick an arm based on the cart. Once you've got that together a dedicated phono could be something to extract that last ounce of performance out of your rig. Top notch electronics can't make up for poor sources, but a good source can make a pedestrian rig sing.(Isn't that why CDs took over in the mainstream?)
I do think the cart is responsible for the sound and resolution of your system and the turntable/arm responsible for extracting the most out of the cart. That's why I started with the TT.

I agree with the above suggestions regarding the phono stage, your budget could get you a good one new or used.

As Syntax points out next inline is the record player.

One that comes to mind thats well within your budget and looks to be interesting is the Well Tempered Amadeus which comes with arm.
I understand the more expensive GT Amadeus is identical to the Amadeus in everyway except for looks and finish.

My niece is replacing her current table at some point soon, Rega P3 and the Amadeus is on a very short list.

Since I have more money in my phonostage (Aesthetix Rhea, $4K MSRP) than anywhere else in the vinyl setup, I really should be in the phonostage-first camp, I guess :-)

But after going from a VPI TNT Mk. II with SDS to a replinthed idler-drive Lenco TT that made a truly profound improvement, I'll stick with my original chain.

And I really don't think the Rhea sounds much if any better than my old much-modded NYAL Moscode "SuperIt" (on MM carts) though it sure is a lot more flexible and user-friendly. Dave