Which CD Players Are both Warm and Detailed

The Sony SCD-1 performs this apparent paradoxical task quite well. I will also include the word 'smooth' along with warm and detailed.

You may be able to find a used SCD-1 for about $2000 or so. Or even the Sony 777es for about $1400 which is supposedly quite similar sonically to the SCD-1.

-IMO

I tried a few players before settling on a Densen B-400, which seems to embody some of the qualities you seek, perhaps falling somewhere between the 'warm' and 'natural' camps. I continue to be impressed by it's sound. Densen's presence is minimal in the U.S., but fairly strong in Europe. I believe Audioasylum has a bit of discourse on this player, if you're inclined to investigate.

Try the Audio Analogue Maestro Mk.1; great for classical and jazz. There's one for sale on AudioGon now and in your price range.

Audio Aero Prima 24/192 .Smooth ,warm , detailed ,inviting.
Also try Audio Analogue Maestro,or Granite Audio.
All of these give great bang for the buck.

I would suggest a used Cary 303 CD player. They can be found on Audiogon for under $1500. It has a great combination of detail and warmness. You will hear everything without feeling a need to turn it down or turn it off. A great CD player. IMHO.