Outboard DAC

Upgrading my system after many years, I'm new to stand alone DAC's.  Question....would the addition of a Musical Fidelity M1DAC improve the sound of my Cambridge 350c or would I be better of upgrading my CD player to something like the Cambridge 651c?  Ultimately I think I want a DAC to play source material from a computer but would love to hear some opinions.  
Thanks, in advance.
Spendor A6, Musical Fidelity M6i, Cambridge Audio azur 350c
Keep the cd player. Buy a good dac. Then you can use the dac for both the cd player and computer.
What Meiwan said. What are you willing to go up to in budget on the outboard DAC? I believe the MF M1 is $699. Are you willing to go up a little bit higher? There are many good DACs in the $1Kish region.
$1100 for the Eastern Electric Minimax Plus. Which has SPDIF coax input as well as async USB input.

It's more expensive than perhaps you're looking to spend, but will serve you better long term. It satisfies your present need and will will work very well indeed when you want to move to a computer based source. Plenty of opportunities to roll opamps too.

If you do decide to go for the EE DAC Plus, use the solid state outputs and pull the tube. It'll deliver a more transparent and dynamic presentation if it doesn't need to keep the tube powered.

I think it's the best value in the $1K price range currently.

For less money, the Schiit Bifrost DAC with USB weighs in at $449, and the CIAudio Transient is a USB to SPDIF converter plus Wolfson based DAC and starts at $699, with an option for an outboard power supply for an additional $329.
I'd like to stay around $700 - $800 because I want to buy a dedicated computer for music. I'm thinking about the HP TouchSmart 320 that I could use without keyboard but still has a lot of storage for music.