I think that a big issue is that while there is nothing wrong with getting a CD player, it may be a bit hard to get anyone who finds that the price for a new player, is necessarily worth it. Mostly because quality of a $500 CD player may not be one bit better than that $80 Blu-ray Disc player.
Which is fine. Spending money on something which looks and feels better isn't necessarily money wasted, but it's important to realize that the drive tray mechanism for almost all CD players is coming off the same assembly line in China that everything else is coming from. Most of it is pretty rickety stuff which will fall apart after just a few years. I've seen top dollar players fail completely due to the drive tray failing over and over again over the years. Such is life.
Knowing this... Knowing that you get zero real world way of knowing how good whatever you get ends up being, I think your best bet is to get something which matches your other system components. The sound quality is very unlikely to be one bit better, but you should get whatever makes you happy overall, and know that if you spend a lot more, you may very well only be buying aesthetics, not actual audio or even build quality.
Still, I would at least look at sites like Crutchfield for some ideas, then if you are on a bit of a budget, I would hit up Craigslist and eBay to see what may be on the used market which you can get.
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www.crutchfield.com
If you are a fan of a particular brand, then that's where I would probably start. I'm a fan of Rotel gear after excellent quality and use over the years, so I would likely lean that direction for a stand alone CD player.
Tested to sound great.
www.ebay.com
There are so many used CD players on the market which come in at a good value, and there are new models which are not incredibly expensive, so it comes down to what your specific tastes and needs happen to be for your setup.
Don't mind the haters, I run into them all the time. People that don't get why you want to do something or need to do something a certain way. At the end of it all, if you have an audio only listening setup without a TV in the mix at all, then getting a CD player can make a lot more sense than using a new BD player, even if the audio quality will be the same. In fairness, I do own a professional CD player from Denon. In absolute fairness... I've never hooked it up, I've gone entirely digital, and when I happen to listen to a CD, it's in my car.