Turntables with better design and with more precision in manufacture can simply get more music out of the groove than a lesser player. Linn Products used to explain it something like this: The only thing that makes sound from the cartridge is the relative movement of the cantilever to the cartridge body, and information in the record groove can be measured in millionths of an inch. Any slop in the main bearing, tonearm bearings, tonearm mount, cartridge/headshell interface, etc., results in loss of information because the wiggles in the groove no longer result in that movement of the cantilever, but is lost to movement in parts that should be rigid. For example, removable headshells, rubber "isolation" blocks, nylon headshell screws, etc., are design features that reduce the rigidity and performance of tonearms.
A question becomes at what price point you get the kind of precision quality that will really make a difference. In Stereophile's survey of several budget cartridges, they included a $9000 turntable/tonearm setup from Feickert as well as models from Linn, Pioneer, and Technics. Part of their conclusion was, "On the Linn LP12 and the Dr. Feickert Blackbird, the Audio-Technica AT95 sounded dramatically more controlled and powerful, more nuanced and sophisticated, than it ever did on the Pioneer PLX-1000 or that stoop-sale Technics SL-1200 I modified in GD9. On the Blackbird-Schick deck, these so-called entry-level cartridges played recordings with a layered, three-dimensional complexity that I thought was impossible at these price points. Quiet musical passages were not only quieter; they were filled with magic little details that got noised over, dulled over, or disappeared entirely on the Pioneer and Technics 'tables."
https://www.stereophile.com/content...nica-goldring-lp-gear-phono-cartridges-page-2
The least expensive turntables that impressed me as getting more musical information out of the groove than others at their price points are models from Rega, and, I think, mostly on the strength of their tonearm quality. I don't think you'll find something like that at the price point you're looking at, but the good news is that music can be enjoyed on much less costly equipment. I have Audio Technica's cheapest model, the LP60X, in my bedroom, and I get a surprising amount of pleasure out of this $139 turntable.