Looking for CD player

If you want anywhere be near "the" best you need seperates. Start with a DAC you like.
I recommend the RME ADI 2 and the Cambridge CXC at your budget. Shop around you can find them both for $1500.
I’m listening to seperates right now - amazing.
Better than Qobuz on 5 diff streamers or LPs on 7 diff carts. To me.

If you want just a CD player, the Musical Fidelity M3s CD is a nice unit and can be had for $1500.  Good internal DAC and nice transport.  I have one that I use as a transport at Audio Shows. This is currently out of stock at the distributor but it looks like they are coming in next week.  

You ought to be able to find some used units in that price range that will be excellent.  An older Ayre CX-7xe is a nice unit.  The Music Room might have one listed or will be listing shortly as I sold one to them recently. 

Otherwise, a decent DAC and a transport like the Cambride CXC would be great.  Pair it with a CXN v2.  A little over your budget but I bet you can haggle down a bit.   

I have a Marantz HD CD-1 which has all current outs, then a Audio Alchemy DDP-1+ PS5, or DDP 2 which also is a preamp
Killer

"...Why spend that much? Just get a new NAD player for around $500. IMO all CD players sound alike!..."

Well I can't agree with that but on the other hand I have used inexpensive players in some systems and I have gotten very favorable results. However, the high-end players do offer much more if your system is up to it. 

from what was mentioned above go with a Rega Saturn if you cna find one for that price.