By Delta, do you mean the kind made by M-Audio? If so, then you already have a good enough sound card. If, on the other hand, Delta is a brand name of "Soundblaster"-type soundcards that I haven't heard of, then you'll probably want to upgrade.
Now, the thing about most mixers is that they mix down to stereo, meaning that you end up with only 2 discrete channels. I believe that's the case with the mixer you mentioned. So, even though they accept 12 inputs, they only output a stereo pair. If you want to record multiple things at once, you CAN do it, but they'll end up on the same track (or pair of tracks) and not necessarily each microphone having its own dedicated track. It's infinitely more useful to have each instrument/mic on its own track.
If your soundcard is the M-Audio Delta series, which one is it? (ie. how many inputs does it have?) I remember seeing a mixer that was a recent release that had an ouput per-channel, and was made with the recording musician in mind. I can't remember who made it or what it was called, but a bit of Googling should come up with it. If, on the other hand, your soundcard is NOT the M-Audio Delta series, you have another option-- buying a new audio interface with built-in pre-amp and multiple channels. That way you can record your various instruments and mics into separate channels.
Greg