At first I didn't get the name, Weezic. Then when I loaded the site I realized it was a play on the name Music. I think the name is clever and catchy. Also I think that the index page looks professional enough to release to the public at this time. You guys did a good job with the looks of it.
Classical music online seem like an overly narrow a niche market, so I would say even though you guys enjoy classical, with such a catchy URL as Weezic it seems like you could expand it into other genres as you iterate.
I think your URL name right now is more valuable than the site. I think you can build a good business around it. Maybe tie the business in with Winamp somehow. Winamp /Weezic kind of works for me.
Having a musical note as part of the logo might be a positive also.