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.
Get a Wyred4Sound DAC-1 and don't look back.
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.
If you go with an asynchronous USB DAC, you won't just have low jitter, you'll have *no* jitter. At just $499 the Halide DAC HD is a Stereophile Class A component with a hard-wired USB cable at one end and Eichmann Bullet RCA plugs at the other. The review and measurements show this DAC to be extraordinarily musical, smooth, and detailed. With the money you save you could get a MacBook Pro and add the remote control for a mere $19.99.

If you want an exemplary DAC that does both, look into the Musical Fidelity V-DAC Mk II, which accepts Toslink, coax, and USB, and the USB is asynchronous. Even if you add the aftermarket Pangea power supply, you're only at $429, which again leaves you more money for the computer, better software--e..g., Amarra--and some tasty 24/96 downloads from HDTracks. The V-DAC Mk II could service your Cambridge player and a computer with USB link.