Blippy, the "beautiful device" you describe is the mixer itself. In this case, the Tascam tape unit, which has all the inputs you describe, is performing that function. Any mixer needs to be cabled to the soundcard, and since the Tascam line outs are two rca's, you need a cable that combines those down into one 1/8" to the soundcard. I just use an adapter cuz that is what I have handy. Primitive? perhaps. Does it do what I need adequately without spending more dough? certainly. OR:
You can spend several hundred or more bucks and get a cool soundcard with all sorts of inputs and just plug your axe or mics directly into that, and use your multitrack software as a mixer. Which is where we'd all like to be.