Welcome, Hanic
As Barometer said, at this point you don't really need a mixer. When you want to add a vocal, you will need a preamp to go between the mic and the line input on your soundcard. Most mixers (though not all) contain at least one microphone preamp, but for realtively the same money as an inexpensive mixer, you can buy a standalone mic preamp that will be of higher quality than the ones in the cheap mixer. That's because with a mixer, your paying for a lot of other extras that you don't need at this point.
When you will begin to need a mixer is if you want to record more than one source simultaneously, and you need to have control over each source separately at that time.
Example: If you want to record your vocal into Cool Edit, and then record another vocal as a background to go along with it, and it's just you doing both vocal parts one at a time, then you don't need a mixer for that.
If you want to record your garage band live, then you wouldn't HAVE to have a mixer, but it would make getting a good recording a whole lot easier. You would want a separate mic for each singer, and a mic for each electric guitar, one for the bass (or the bass could go direct to the mixer, but that's another discussion) and at least a couple of mics to pick up the drums. Assuming that your PC soundcard has only two inputs (as in L-R stereo), you would want a way to combine (MIX) all of those sources (mics)into those two inputs, controlling the level of each source relative to the others. That way the guitar isn't way louder than the vocals, and it doesn't all get drowned out by the drums. You control how loud each instrument or voice is, as well as adding or subtracting bass or treble or midrange for each to suit your taste.
So, to answer your question, the only time you need a mixer, is when you're recording more than one thing, and they have to be performed at the same time.
Have I thoroughly confused you? I'm good at that.
Remember, it's all about having fun. Good luck.
