If you had to choose between a recording in which your playing was better or a recording in which the quality was better, which should you choose?
I have two recordings of the same piece, one I recorded at home with my camera and it sounds better to an extent but the sound quality is not so good. The other was recorded live and has better quality but I guess I was nervous because while it’s not bad, it’s not as good as the other recording.
I am a little nervous because all my symphony friends have had professionals do their recordings and my family can’t afford to do that. I don’t want to submit something that might look unprofessional…
I would do whichever one you feel you sound better in! The college can not ethically put you down for not doing a professional recording, as I am sure they are aware not everyone can afford the professional recording session. Do whichever one shows your talent better and I wish you good luck! 
You can buy a decent USB microphone for $50 or less. If you are into music enough to be submitting recordings, maybe it would be a good investment.