NAD C565bee/Rega Apollo vs. DAC MHDT Paradisea 3

After years of primarily playing vinyl, I'd like to add a digital source to my system; McIntosh MA-230, Thorens 320, Focal 807v. The idea here is that I can play CDs as well as mp3s from my Apple computer. Doing some research and checking my wife's approval rate (WAR), it boils down to the following two options:
1) A NAD C565bee or maybe a Rega Apollo.
2) A cheap cd player in combination with a MHDT Paradisea 3 or a Cambridge DAC Magic.
I would appreciate to hear on how a decent cd player (e.g., NAD/Rega) compares to the DACs (e.g., MHDT/Cambridge)?
Both the NAD and REGA are outstanding. Not sure how much, if anything, will be gained by putting a DAC in. The Rega prides itself on a pure Redbook playback.
Thanks for your response. I guess what I meant was either option 1 or option 2. A more expensive stand alone cd player OR a cheap old cd player in combination with a DAC. Any thoughts?
Not sure if this is useful information to you or not... but I have a NAD565BEE connected to my computer via the optical IN on the CD player thus playing my computer through the CD player dac. I also have a Asus Xonar Essence sound card which is supposedly pretty good. The asus has regular RCA analog outputs. The sound from both is almost the same, but the sound through the NAD is definitely better. I did A/B testing to confirm this.

Also the USB reader on the NAD does a great job. Mp3s played off of a flash drive sound as good as those same mp3s burned to an Audio CD (not data).

I have been very happy with my NAD565BEE. It was a refurb from Spirit Sound.. Hard to beat the price...
NAD 565BEE is a good player. The NAD built in DAC is quite good and you can connect your computer to a NAD 565BEE's DAC as mentioned above. I do not know if Rega Apollo has a digital input so I cannot comment on that.

MP3 files that I converted from WAVE files (regular audio CDs) and saved onto my IPOD connecting to my NAD amps when played back for some reasons do not sound as good as the regular CDs when I play them via my cheap NAD 545BEE.

To my ears, a regular CD playing thru a regular CD player sounds more analog more real than a lossless file song downloaded from Apple website. MP3 files are too much digital but it is just my $0.02.

If you are using the analog outs (headphone jack) on the ipod, then there is your problem.. The DAC on the ipod isn't as good as the ones in the cd player.
The Apollo is far better than the NAD to my ears. I've owned NAD CDPs in the past, and currently own an Apollo. The Apollo beats it in it's PRaT and just overall musicallity. I'm a big analog fan, so take that as you will.

Haven't heard the DACs you mention to compare.
I own Nad565bee cd player & it does an outstanding job making sense of music.
The balance & timing are dead on,much improvement over Sony XA5400 cd player redbook