The cartridge, tone-arm, and phono-amp are more important than the turntable, in my opinion.
The above assumes that you buy a reasonably good turntable (not a Walmart turntable).
And professionally dialing it all in is a top priority, or it will be mostly money down the drain, no matter how good the choices that you made were.
Putting your turntable on a vibration control platform is also critical. There are third party footers that also do wonders for controlling vibrations, even if you think that you have none.
And finally, the specific pressings that you play can either make your turntable shine, or bring it to its knees (most will do the latter). An unfortunate reality is the nearly absent quality control in the pressing plants, and the incompetence with the studio's mixing and mastering engineers.
No dream rig in the world can fix defectively produced pressings (and 80%+ are defective, to my ears).
Even on pressings with to-die-for sound quality, you will rarely hear all of the songs have that sound quality (I have never heard all songs have outstanding sound quality). So that points to the incompetence with the studio's mixing and mastering personnel, when one or more songs on a side sound amazing, but not all of the songs on that same side sound amazing.
Digital has the same issues. One or two songs on an album will sound fantastic, and the rest fall short.
Back to the cartridge choice:
My first cartridge was ¼ the cost of my turntable, and my phono-amp was ½ the cost of my turntable. Both the cartridge and the phono amp were poor choices.
Upgrading them helped a great deal. Then I had my local store's turntable guru dial in my turntable's tone-arm / cartridge, and that was revolutionary (like my equipment just tripled in price).
Approximately 5 months ago, I upgraded my cartridge, again, and that helped, again, but not nearly as much as my initial upgrades, vibration control remedy, and professionally dialing in everything by a turntable expert. And with white hot stamper pressings, my vinyl sounds great. But I have a small collection, because I buy and dump most of my purchases. It is hard and expensive to land great sounding pressings, and I stopped purchasing pressings nearly 10 years ago, as it got too expensive to keep buying defective pressings.
Never purchase heavy vinyl, or half-speed masters, or mixing and mastering supervised by [fill in famous artist name] pressings, or re-masters. None of them sound good, in my experience -- all are cash grabs. And nothing, since approximately the year 2000 sounds good (I believe that the vinyl formula changed).
I can't speak for specialty pressings. I purchase popular music from the 1960s through the 1980s.
In my local high-end store, they have two wildly good turntables in their "big" room. One costs $15,000 and the other more than double that. Both sound virtually the same to me, except whichever one they happen to have a better cartridge on always sounds better. I have heard Clearaudio, DS Audio, Hana, Lyra, and Benz cartridges mixed between their two outstanding turntables, and the one with the better cartridge always took the win.
If you have a revealing stereo, get a Townshend Seismic Platform, or Stack Audio footers, or AV Room Service footers, etc, and your ears will thank you.
Also have a professional dial in your turntable / tone-arm / cartridge.
A good turntable matters. But the above equipment (including the phono-amp), cherry-picked pressings, and dialing it all in is more important, to my ears, than going to town on a more expensive turntable.