If i wanted to record some music I was playing on a piano, perhaps some vocals as well, what is the cheapest piece of equipment I could do this with? The quality doesn't have to be good, it just has to be able to record and connect to a computer.
You can get basic recording software for your computer for under $40. Then you'll need a microphone with a 1/8" jack to plug into the computer. $10-20 for that.
I think there are some free softwarez for recording out there, shareware and the like. Wasn't there a free version of some Pro Tools program? Anyway, here's a free one, haven't tried it but for basic recording it's probably ok: http://www.kreatives.org/kristal/
Get a mic like MasterOLightning says for about 10-20 bucks and you'll be set. Don't expect any quality sounds though...
+1 for the Shure SM57, it's a bit pricier than one of those cheaper computer mics but it'll last a lot longer & can more easily take the kind of volume you'd get from a piano. They're tough mics too, they can take a beating.
I wouldn't spend a lot on a mic until you are sure you're serious about recording. Otherwise you're better off spending on something like music lessons.