Develop a hierarchy for phono playback

I put the tonearm first, not for sound quality, but for reliability and ease of adjustment. I built my own turntable using a thread powered external DC motor and a sandwiched bolted together pair of 1/4" thick pieces of transparent florescent green acrylic sheets I cut to shape on a band saw. They are tightly bolted together and they are screw-adjustable in a garnet plate sitting on vibration isolating hemispheres. I have a premium spindle ceramic bearing and a large acrylic platter from spare parts. This is simple so it can be fourth. The cartridge is second because it is critical. I use a moving magnet Ortofon Black cartridge because I do not accept the way moving coil cartridges cannot be repaired after they wear out in about 1000 hours of use and cost so much that it makes playing records cost more than a streaming service. Third is a simple vacuum tube phono preamp and cables that make a reliable connection that sounds best when the pins make a clean contact. 

Nice try, @billstevenson , but not practical or likely applicable.  Most purchases are budget limited, so trade offs until deep enough pockets to optimize individual components.  For instance, a quality tonearm may be similar in cost to an entry level turntable+tonearm combo.  Also, with many carts, phono stages, etc. how do you choose? At what level is acceptable? It’s not black and white.  

Phono stage first.

Everything else has to go through it.  Not sure why folks don't see the logic behind this.  You can have the greatest TT/Cart ever but running it through a mediocre phono stage only gets you mediocre.  A great phono stage will let you hear the changes you make behind it.

Get the most phono stage you can afford.

SWS applies. 

synergy-weakest link-subjectivity. 

If I had to pick one: the cartridge. It touches the groove. You need to preserve your collection. 

There will be no consensus. 

@theflattire You can have the greatest TT/Cart ever but running it through a mediocre phono stage only gets you mediocre.

The same argument applies to each component further downstream until you get to the speakers (or hearing aids!) But what does it profit you to have great speakers with a lousy source?—you just hear well reproduced errors. And each step along the chain may magnify the errors it receives from above, so that by the time that signal gets to those speakers it is quite degraded. That's why I say the source is paramount.

But this assumes that all components are roughly equal in quality. The weakest link in the chain makes for a bottleneck, and if there is one, it should be addressed first. This year has seen me replace a cartridge, phono stage and pre-amp. Each made a difference, but you'll be glad to hear the biggest difference came with the phono stage. I'd say that was because its predecessor was letting the side down, not because a phono stage is automatically most important!