This is best put under "How-To Sound" section
Mic: I used to use a computer mic to record vocals. That was about 5 years back. I just use my software to boost up the volume after I am done. You can actually listen to how it turned out on my myspace account:
http://www.myspace.com/thehouseofanonymous
Click on the song called "Catastrophe".
Of course, you can probably tell that it's not gonna give you teh best sound. But it doesn't sound the worst either. In fact, all the recording you hear on that page are done either on computer mic or a cheap karaoke mic (I have yet to upload a song that I use my SM 58 with).
Anyway...
If you are looking for a condensor mic, that would require phantom power, which a mixer can provide for you. These days, however, you have the option of a USB condensor mic, which doesn't require a mixer to boost it. Just plug in to PC and sing.
Another option is to just boost up the volume of your recording by using the DAW software you are using. This method is not advisable, though, cos when you boost up mic volume, you are also boosting up all the background noises that you record into the mic.
You can, however, minimise the noise by employing some simple acoustic techniques. I use to cover my mic with a sweater to reduce pops and back ground noises. You can also cover yourself and the mic with a heavy blanket you record. Crude, may seem silly even. But it works.
Let me add the MIDI part in a while...