Apple sells GarageBand for about $15/£10 currently. At this price point, what do I gain over something free like Audacity?
My use-case is recording myself singing and playing guitar for home use, or for sticking on the internet for nobody to see.
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Although Garageband is definitely good value for it's price if you just want to record something you can just as well use audacity.
Garageband has a large library with sound effects and good sounding instruments like drums, strings,trumpets etc. so it's a good (and cheap) place to start with if you want to compose something more than just your voice and guitar, like adding a bit of rhythm (drums) or something like that.
If you consider a professional career though, I would suggest something like propellerheads reason (although I must admit it's a bit price - about 400€). I believe you can download a demo here http://www.propellerheads.se.
The one thing Garageband gives you in your use case is:
It is very user friendly for all your basic tasks, and offers you some nice additional features, like backing and drums.
Audacity is cross-platform and for the basics is not too difficult to use, but for anything more than the basics can be tricky to configure, and it sounds like you do not need that.