Here's a quick link reference list for some of the product and topic areas related to computer audio recording tools, software and hardware. I've highlighed either recommended products, or inexpensive products I have used myself with good success.
Microphones:
Shure SM58 from Guitar Center or Musician's Friend
Small Mixers:
Behringer UB502 (sorry, no longer available)
Behringer UB802 (sorry, no longer available)
The UB502 and UB802 has been replaced by the newly introduced Berhinger Xenyx line, such as this one.
Behringer Xenyx 502 from Guitar Center or Musician's Friend
Behringer Xenyx 802 from Guitar Center or Musician's Friend
USB Audio Interface:
Behringer UCA202 from Guitar Center or Musician's Friend
Software:
Audacity (I use the 1.2.x version available here, the 1.3 line isn't stable yet in my experience)