Looking for a CD player

I love my Rega Apollo player, and you can get a new one within your budget. It gets very good reviews. I love the top-loading feature, as there is no motorized tray to go bad.
https://www.stereophile.com/content/rega-research-apollo-cd-player

Conclusions
Forced to sum up the Rega Apollo's sound in a sentence or two, I would write: This player has a sonic brilliance—a clarity of detail and of musical line, allied with a spatially up-front presentation—that enhances musical engagement. The Apollo doesn't gladly suffer bright or timbrally threadbare CDs—something I dimly recall being even truer of the original Apollo—but with most discs I tried, it provided enjoyable, involving, nonfatiguing sound.

My thoughts on value are even more concise. As with other Rega products—their entry-level tonearms come to mind—few other audio components of my experience, and no other contemporary CD players, offer so much music for so little money. Unless your system has an egregiously bright sound, you can't go wrong with the Rega Apollo. And if your heart is set on spending $10,000, go ahead and buy nine of these and spread the love. Robustly recommended.

Another really good CDP with preamp out and DAC input is the Cambridge Audio 851C. I have one and it sounds very nice and not bright whatsoever. It is a fairly revealing player so poor recordings are still going to sound as they are. Change out the two fuses which I did with the right power cord it’ll be tuff to beat and for what they go for used these days it’s definitely a player to consider. I also own a stock Oppo 205 and the Cambridge is more refined. Still would consider separates but for what a used Cambridge 851C goes for, you could start there then later add a DAC which is what I did, but don’t underestimate the 851C on its own. It’s also nicely built. I would think going through your Primaluna will sound great as the Cambridge is an open/transparent player. Also balance out sounds better to my ears if you have that option.

I use a Cambridge CXC CD transport and Bel Canto 2.7 DAC and it does sound good. Got the DAC used. I'm not entirely thrilled with the CXC. The remote is absurdly large- has controls for a whole system and only a few work for the transport. But more importantly, it fails to play some CDs from legit publishers and appears to skip easily due to superficial scratches/dirt.  Just doesn't seem as robust as other CD players I have had.

I am a big fan of Bel Canto, and not just the DAC.

The remote is absurdly large- has controls for a whole system and only a few work for the transport.

I don't mind the remote, but I'm currently still using the CXN as my DAC/streamer. In that format I think the size is more comfortable. But I could see it being really annoying if you're only using the CD player. 

If your CD player has a digital coax out, I would buy a Schiit Yggdrasil GS at $1599. I play CD’s with a Marantz U7007 Blu Ray player with my Yggdrasil and its sounds really great.