Two thousand bucks buys a very nice turntable. However, you're going to need an amplifier, pre-amplifier with phono stage, receiver or integrated amplifier with a good phono stage for a turntable. Sound quality is a rather nebulous term and will depend entirely upon the components used in the chain (e.g. amplifier; phono stage; speakers; cartridge; records; etc.). My advice would be to listen to as many turntables in your budget range, as possible, and make certain those auditions are performed using components as similar to yours, as possible. I would bring records you are very familiar with, as well; clean ones in good shape. Shops usually use their best componentry and LP recordings in auditions in order to impress. First pressings, virgin vinyl, re-pressings from original master tapes, etc. are going to sound much better than bargain basement, tag sale, cheap thin vinyl reissues. You should also bring LPs that will challenge the turntables & cartridges you audition (i.e. music over the entire frequency ranges from high to low bass). One recording I enjoy using for this is: "Tubular Bells" by Michael Oldfield. Regardless, you should use music you are already very familiar with.

This is a somewhat dated article but will provide a quick & dirty basic primer:

https://www.nytimes.com/2012/05/31/technology/personaltech/the-secrets-of-a-high-quality-vinyl-record.html

If you haven't already, you should spend some time reading Michael Fremer on Analog Planet (analogplanet.com). If you're really serious about this, he will quickly become your new best friend.

Here's a small sample of quality turntables in your budget range you might want to consider: Pro-Ject; Mobile Fidelity; Rega; Clearaudio; Marantz; Music Hall; Thorens.

I started with turntables as a youth (that was all there was) and added a digital end when they became available. Back then digital could not touch analog. While things have come a long way, in general analog still has the cost advantage.in general, typically you have to spend about 2 times more on a digital end to rival analog at most audiophile levels... up to and including hundreds of thousands for each end. The center of most all audiophile systems is the preamp. So the digital end will consist of a DAC and music server... the analog end will consist of a turntable, arm, cartridge, and Phonostage. In my system my digital end cost about $41K and my analog end cost abought $31K... I give the advantage to the analog end (Linn Sondec SP12). You certainly will not be buying something at this level... more like Rega, or Pro-Ject is the place to start. You want to make sure to have a good Phonostage. Most audiophiles choose separate boxes for each function as few of us could ever afford what we wanted and choose to slowly achieve our goals over decades. There is a huge learning curve in how to choose compatible and complimentary products, what you like, and understanding the qualities of sound. In general, spending a lot more is usually worth it, and expenditures of 2x or 3x in upgrades get you a “Wow, that sounds a lot better”. If your objective is “cost effective” go for used equipment or find another hobby. As all of out wives say, “there are regular dollars and audio dollars” . One audio dollar equals 10 or 20 regular dollars. I’ll look for the best deal to save a couple buck on a food processor and spend $4,700 on a set of speaker cables without a second thought. But the incredible rewards for this pursuit and the musical enjoyment far exceeds the cost.

After giving your interest some thought. If you want a good start on a very good sounding analog end I would stretch to $3,000. I would spend $1,500 on a good used phono stage (original cost around $3,000), then about $800 on a good cartridge, and $700 on a turntable / arm. I think this is something that would probably sound better than about any $6K - 10K digital end and gets you out of the mid-fi equipment range. Hopefully your other equipment is up to it. Even if it isn’t then you can grow into this equipment. The source really sets what the rest of your system will sound like... garbage in, garbage out.