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