What features should a good CD player have?

If your buying decision is based on features and specs you will be disappointed with your purchase.

Power supply
Disc drive assembly/Transport mechanism
Analog circuitry

Having owned a lot of CDP with digital inputs and volume control, I can tell you with a high degree of confidence that at $1,500 (even used) you will not find one that is going to be that good. One with an analog volume control is going to be even harder to find at this price point. If you really want to take this route, start by adding $1,000 to your price then look for a Levinson 39, 39S or possibly a 390. Double your price and you can probably get into a 390S.

On the otherhand, you should be able to find a pretty good CDP without digital inputs and without volume control that is very good at this price point.

Personally, I would recommend an Esoteric (at this price level you are looking at a DV-50). But my concern with recommending that is due to the fact that you have a Jolida and as a result, I am assuming you are looking for something on the warm side (versus detailed or highly resolving).

Maybe you should consider getting a used DAC at this price point.

If the Jolida has digital out, get a benchmark dac and a good digital cable. You will eventualy get a music server and will then already have the dac and good a digital cable and didn't just invest in a cd player.

why not just check out some of the mod Wright Sony's that pop up now and then...

If you are going to consider the Benchmark DAC I would insist on an inhome trial/audition and while doing that see if you can even find any improvement with this DAC vs. your existing CDP running direct in a double blind test. Not a different sound, but an improvement. My guess is that you'll have a DAC but you won't end up with an improvement in sound quality. You can run the analog output of your CDP to your preamp and the digital output to the Benchmark and then the benchmark to the preamp. Have it volume matched and listen back and forth for a few days, not knowing which input the pre is set to for careful listening. But switch back and forth from time to time.

My point is that you can do a lot better than this DAC for your $1,500, buying used.