CD Player to match Classe amp and Kestrels

Classe CAP-100 Integrated Amp
Meadowlark Kestrel Hot Rod Speakers
Synergistic Research Alpha Quad Speaker Cable
DH Labs BL1 Series 2 Interconnect
NAD 521 CD player (1997)

A relative newcomer to this world, I have upgraded everything in my old system to what you see above. The last piece is the cd player, which I hope to replace for under $500 used.

I have already read the excellent posts suggesting Cambridge D500, Musical Fidelity E624, Rega Planet, and others, and I am asking now for fine tuning, if you will.
My tastes mostly run toward acoustic jazz/classical and I enjoy the musical sound of this system. I am wondering what CD player will best complement it and maybe add a little detail.

I am also wondering whether my (obviously) limited budget right now will really gain me that much improvement over the NAD. I want to replace it with something I can keep for many years. Any thoughts are appreciated.