I don't know exactly what kind of audition this is, but if it is one of those "please send a disc and we'll tell you if we want you to come and play later" kind of auditions (or maybe some audition for a scholarship or an exchange year at another school) you need not go through all that much trouble. Just get something decent enough as to not distort the sounds you make to a point where you actually can't hear whether you can play or not. I did that once, when I messed up at the recording session, meaning I had to record myself on my cell phone later on... sounded precisely like I was playing through a bad phone..! Still, it was the only thing I could do, so I sent it. Then the school called back after a while and asked me to make a better one, which I did. Again, in a hurry, and on a Macbook with no external mike, but it was good enough for them this time. They just needed a little better sound.
Now, here's how I do it these days. It doesn't seem as if you have a recording machine for your practising? If this is something that you've been thinking about getting, get one, and use that. I think that for instance, a Zoom H2 is listed at about €200. That's where thay start, but you don't REALLY need amore expensive one. It'll be good enough for the audio. Then just borrow somebody's handycam (maybe your school can even provide you with one?) but even a computer with an average web camera will do. I think most Macbooks are equipped with one that will give the viewer a fair idea of how and what you look like when you play. I think a simple program such as Movie Maker would be enough then to mute the audio from the vid and put the one from the recording machine in its stead. I've done all this myself, apart from the Movie Maker bit, and the quality hasn't provoked anyone. Yet.
What I would avoid is recording on minidisc, or any other format that's difficult to copy to your computer. Like tape. You want something that creates a proper audio file already on your machine. A minidisc is fine for practising, but you'll get problems converting the music. I can be done, but... MD's are very 2000 anyway.
Now, if it is a bloody serious audition, with NO live auditioning, you might want to get outside help... but in nineteen cases out of twenty, I reckon this is enough.