Will62
Sorry about derailing the thread with the DVD/Blu-ray player idea. I understand your need to keep things simple. I did it for a couple of reasons. The first one is for other people searching for a CD player so they can have a "more rounded" list of options.
The other reason I suggested using a free or low cost DVD player was that you could spend more (or all) of your budget on a better DAC.
You said you have an older CD player with a toslink output. I would use that and look into a Schiit Bifrost2. It has one nice feature for CD playback: polarity inversion. Some CDs have the polarity reversed during playback. Unfortunately at $700 it is more than buget of $600 not knowing how flexible you are on that.
To sum it all up you will get the best quality of sound from your CDs using a transport and a DAC (for the least amount of money). A dedicated transport can cost around $500. DVD players can do the same thing for less. I am using an old DVD player in my main system without a display (tv). It doesn't even have HDMI, but it does have buttons. I just pop the disc in and press play. Did the same thing at my parents house when I set up a stereo system in their living room (no tv there either).