What is the chain of importance in analog system ?

I think this analog analysis is a tad microscopic. The most important piece of matter is the record itself. If it is terribly worn out, scratched up by a cat in heat, cracked or have moguls for warps it really can't sound good. It relys on - no good great indiffferent or terribly bad cartridge, or arm, or cable, or phono stage, plinth bearing spindle shelf footers and dampers will be able to fix that.
Trust me I do not edorse or not endorse blue white hot stompers or whatever. The record firstly must be in good shape.
If the music content extracted from the vinyl or polymer, or wax etc. is something you really dislike, nothing in any part of the chain that you change will matter. In all probability you will not even trouble yourself, to play your rig if the music sucked.
No matter if a system happens to have utterly perfect synergy, is an assault on the; cost is no object, the top of world, state of the art, all time best equipment. Hearing a dreadful bit of cacophany that someone accidently decided was music, and do actually enjoy.
May send you howling the blood curdling screams of a severely tortured soul, at mach speed out of the room.It can never be compensated for ( watch it-that sounds like phono stage stuff) by any gear known to man or alien, whatsoever, period, end of story, good bye.

If I were to start over again. The entire chain would go like this. For analog only playback.

A#1. MONEY.
1. Turntable.
1a. Consider 2 arm table.
2. Arm.
2a. Additional arm to be mounted later. Stereo/mono play back.
3. Phonostage.
3a. With 2 inputs.
4. Cartridge.
5. Preamp.
6. Speakers.
7. Amp.
8. Cables interconnects & speaker.
9. Power Conditioner.
10. Power cords.
Records between everything.
IMHO.

thanks for the input guys. So, if we are to put this in reality, maybe you guys can suggest some good combos to start with based on the theories and experiences you guys have.
maybe a tt system w/ cart, table, arm, phono stage and tonearm cabling for $5000-$8,000.

Ex: Lyra Dorian-> VPI Classic with original tonearm-> modwright phono stage-> nordost tonearm cabling

this is getting interesting.

"maybe you guys can suggest some good combos"

That's the way to do it!

As has been stated above, everything is important.

It then, IMO, becomes a question of value for money. As a result of that, it becomes a question of where you focus your money.

Once again, IMO of course, it then goes this way.

Good turntables are not cheap (even used). Good phono stages are not cheap, particularly for LOMC (even used).

Good tonearms can be had at a more reasonable cost (new or used).

Good cartridges can be had at a more reasonable cost (new-I wouldn't consider buying a used cartridge personally, but to each his own, although I do think a "tweaked" cartridge is the way to go).

Therefore, IMO once again, strictly on a cost basis, the following formula should apply:

Tied for first (within reason): Turntable and Phono Stage
Second: Tonearm
Third: Cartridge