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.