Will A new DAC improve the sound of my Cary 306/200 CD Player

I would say it's very likely the sound will be different, and it's up to you to decide if it's an improvement or not :) That said, if you can demo anything, or if anyone does like Schiit where you can audition for up to 15 days and send back for full refund (minus shipping, unfortunately - cost of doing business I guess), that's what I would suggest. Musicdirect, Amazon, and other places can do so, and a local dealer might as well, but just be clear on the policy if you attempt to do so.

It's a little over your price range but the newest Gungnir from Schiit reads like a terrific value for around $1250. I have it's bigger sibling, Yggdrasil, and it makes redbook CD sound absolutely glorious. 

I have the same CD player as you and over the summer bought a gently used PS Audio PerfectWave DAC for about a couple of hundred dollars more from your price range.  The synergy sounds great to my ears.

I'd recommend trying an Audio Alchemy DDP-1 with the PS5 power supply. I've been running this combination for about a year & it is remarkable for the money. I placed a link below in case you're interested.

https://www.audioadvisor.com/prodinfo.asp?number=1ALDDP1P5

 

Note that you are not listening to the DAC, but the output stage. You may be able to find a more modern DAC, but you will have to pay a lot for an output stage which betters the one in your CARY.

kjl1065
Will A new DAC improve the sound of my Cary 306/200 CD Player

No, not for PCM Redbook, unless you spend quite a bit on the newer discrete R2R dacs, like a Holo Spring, or Denafrips Terminator, TotalDac ect ect.

Your Cary has 8 x PCM1704 d/a converters (best there was) and a PMD200 hdcd filter chip (aslo best there was), this is about as good as you can get for R2R Multibit PCM replay.

I had the similar 303/200, about the only thing you can do is get some one who’s good, to improve the I/V stage and output buffer, this will really make it sing.

I did a whole thread on this at diyAudio using zero feedback stacked AD844 transconductance chips for I/V duties and OPA627 output buffer, it was very good in the end.
https://www.diyaudio.com/forums/digital-line-level/227677-using-ad844.html

And go direct to poweramp and use the volume control it’s got.

PS get a new spare laser/mech for it before they’re obsolete. Philips VAM1202
https://www.ebay.com/sch/i.html?_from=R40&_trksid=p2053587.m570.l1313.TR3.TRC2.A0.H0.TRS0&_n...

Also, do not sell this machine, I had to get a  $20k LINN CD12 before I could better my mod'ed 303/200 and no dac that plays DSD (Delta Sigma based) can touch it for PCM REDBOOK replay

Cheers George