Upgrading to a stand alone DAC

I will add to the Schiit Bifrost 2 recommendation.  I have the same NAD CD player as you and was simply stunned at the improvement made by switching to the Bifrost 2, which I later upgraded to the 2/64.  Better tonal quality of the instruments, better soundstage, better bass definition, and better definition overall.  And, it is only slightly more than half your budget.  A used Yggdrasil at closer to your budget most likely would be a further improvement.

I have played about with stand alone DACs since I bought my first Arcam Black Box way back when.  I have found that sound quality is not necessarily directly related to price, so auditioning is important.  I am currently using a Moon DAC in one system, a vintage Classe DAC1 in another, and a Hegel in another and they are all very good.

You should have a little talk with yourself about what qualities you really prize in music:

-- Are you thrilled by more and more apparent resolution?

-- Do you want deep, percussive bass?

-- Do you listen to classical music and appreciate the sound of mass strings?

-- What is more important in audio-reproduced sound: excitement, or timbre and tgone that are close to the original instruments/voices?

When you go with a standalone DAC, you can certainly get certain sonic benefits compared to a CD player. But you'll get more bang for the buck if you pursue a type of DAC that suits your tastes.

I was an analog guy from way back. Loved turntables, MM cartridges, and vinyl sound. I wrestled with digital audio for decades, never really satisfied with certain aspects of digital sound--namely the artificially emphasized transients, thin/non--existent harmonics, and notes presented as 2D cardboard cutouts, with little of the roundness of tone and spatial cues I hear in music performed IRL.

Until I found NOS (non-overampling) digital, also the very closely related tech, multibit digital. Both are old digital techniques that were long ago superceded by the most cost effective delta-sigma technology. I'm not an expert in what's under the hood of each, but I can tell you that the first time I heard NOS digital, my entire relationship with digital audio changed. I've had 5-6 DACs total, and now have 3 NOS models of differing cost and features. They all sound more musically realistic and lifelike than any delta-sigma DAC.

i just ordered a holo cyan 2 dac for a little less than your budget. i currently hve a gungnit mb and want a new sound.

Yes you will hear a significant improvement at this price point.  There are many budget friendly DAC's which will greatly improve your sound.