You need not spend oodles of money for a good sounding CD player. As in most things audiophile equipment wise, sound quality depends very much upon the components in the chain. If you have a good DAC in your amp, integrated amp, a good external DAC, etc., I suggest thinking more in terms of "transport", rather than "player".
By way of example borne from personal experience, I have a Marantz CD6005 that I purchased new for less than 500 bucks over 11 years ago that sounds great with my McIntosh integrated amp. Several years ago, I A/B'd it against a 3500-dollar Rega CD player, using the same integrated that I have, the same speakers and several of my own CDs that I am very familiar with. According to my ears and those of a good audiophile friend who was with me at the time, the Marantz sounded every bit as good as the much more expensive Rega in every respect. More recently, I A/B'd the Marantz in my own 2-channel system at home using its internal DAC against the McIntosh's DA1 internal DAC. The difference in sound quality or fidelity was so infinitesimally small, if indeed one existed at all, that I elected to use it as a transport rather than switching it back to a player. My wife actually preferred the sound of the Marantz DAC whereas my ears thought the MAC's DAC offered just a tiny bit more bass extension. Shortly after these experiences, my audiophile friend purchased a Marantz CD6006.
One last two cents worth of advice. Prior to purchasing the CD6005, I auditioned it against two NAD CD players, one in its competitive price range and one which was a couple hundred bucks more expensive. After a matter of seconds, it was clear to my ears that the price point competitor wasn't in the same ballpark, sound fidelity wise. As for the one that was a couple hundred bucks more, it only took my ears about a minute or so to decide I was bringing the Marantz home with me. So, again as in all things audiophile, if possible, I would advise that you do some critical listening to the components you are interested in prior to making a decision.