Like most threads here, everyone has their own sense of what constitutes a good piece of equipment. I believe that some of this involves personal taste, component synergy, and I suspect that it is mostly due to having heard few systems. The most important question are what is your budget and what components other than cd player are you using? Perhaps I missed your statement of budget, but considering that you are not looking to upgrade one of the most critical components, the DAC, I’m guessing that you want to keep costs down, in which case you have some excellent suggestions above. If you want to go to the next level then there are some members with extensive experience at various, including high levels of build. @ghdprentice above is in that category and probably others.
I’m not one of the experienced few, but over the last year I did cycle through various gear. I discovered that my sense of what sounded good and what I would recommend has changed as I discovered unexpected reproduction improvements. In my opinion general computers are not good streamers, but they do keep cost down. Roon is a widely used program for organizing stream content. You will then need a Roon subscription plus a subscription to a music service. Roon requires a Roon server and separate streamer, or a streamer with built in Roon server. I use an Aurender N20 streamer, which isn’t Roon based and uses the Aurender conductor app running on a mobile device, but it doesn’t require an external server. I still need a subscription music service. I have all of my CDs ripped and stored on my N20. The playback is, to me, phenomenal. So, consider buying used to maximize results. Also, this allows you to upgrade at a latter date without losing 50% of the new value.