If you're creating an entertainment website and you're not a designer, you'll need help not only with the logo but also the website design, fonts, colors, icons, advertising, and everything else, which all need to coordinate.

If this is a professional site then the designer's fees are part of your startup costs. If it's an amateur site your best bet might be to get a design student at a local college who'd be willing to work for free in exchange for getting a nice portfolio piece.

Not trying to be unhelpful, but designing a proper logo is a big job and requires more info than you've given. If you're just looking for some quickie ideas, google Music Logo (or whatever words best describe your site) and click the Images tab, and you'll see hundreds of existing logos (some good, some bad).

And why would any designer want to do this for free?