An op-amp can be used in many configurations, two of them you mentioned were inverting and non-inverting. Depending on the gain you desire phase inversion may or may not matter. The issues that come into play are stability, gain, and bandwidth. For instance if you want a unity-gain circuit, the non-inverting version will require no resistors whereas the inverting version requires 2 resistors. You also get more bandwidth out of the non-inverting unity gain configuration. Perhaps somebody else can suggest suitable amps though it is probably not too difficult to find them designed specifically for audio (for video they definately exist and are labeled as such).