Hey guys,

I've been saving up to get some gear to record, but first I need to know the very minimum I need to record, so I know what to get when I have the money. What I was thinking I could do is;

Mic'ed up instruments > Mixer > Input on computer > Recording software

Do you reckon this would work?

How are you going to connect the mixer to the PC?
Sure. It can be done. I've done it before. It's not always the cleanest sound, but if you just want to get something into the computer, it's cheap and easy. I used to have a slight problem with hum - most likely caused by groundloop. Even though I plugged everything into the same outlet, still had some hum. I finally got rid of it by purchasing a Tascam US-2000. This is a USB interface with Cubase. Absolutely zero hum and sounds great.
it will work, but it wont sound great. your onboard sound card is not meant for recording, and it isnt going to do a great job of it. instead pick up an audio interface and use that instead of your soundcard. get one with the number of inputs you need, and then drop the mixer. most of the time you dont want to do your mixing on an external mixer anyway.

for recording anything that has drums, i would go with either of these:
with my personal preference as the profire.

if you are only recording 2 inputs at a time (ie. keyboards or maybe acoustic guitar) you could go with something like these:

or for cheaper:

and thats just options from two brands. there are lots of other things out there, but that just gives you an idea of what you should be looking at.