New or Old CD Player?

The EAR Yoshino Acute Classic is the best I've heard for REDBOOK cd's.  The most analog sounding I've come across.   Finding one used would be within your budget most likely.   The Acute Classic is the most recent version from EAR, having done Acute 1, 2 and 3 over the past decade or so.  The ACUTE CLASSIC does sound improved over the prior versions, so there are some advancements in sound that would be best to get latest versions of cd players if funds allow.  Digital has improved quite a bit over the last decade, even in strictly redbook cd players.

If a quality and statement piece CD is what you want, you can't go past a Yamaha CD-S3000. Look at the specifications! This is not a bit of this and a bit of that OPPO or the like. This is an out and out top end CD/SACD player.

I would opt for a CEC TL-5. This is an analog sounding transport that is belt driven and gets absolutely rave reviews for under $3K. Go through a dealer. Don't buy off Ebay.

Marantz SA10s1

imgoodwithtools
 only intend to play Redbook CD's and want a one-box solution.
 

If you want one box players, not dacs, these are the ones.
For finest Redbook replay, as there are no new players built around these dac chips, you want players that used the best implemented (at the time) 2R2 Ladder Multibit Dac in them, the PCM1704"k" selected.

These are my 3 in order, there are more.

1: Naim CD555 with 555 power base
2: Linn Sondek CD-12 MkIII version that has 4 x PCM1704K and PMD200 
3: Esoteric X-01

Cheers George