There is a right and wrong way to handle sound in Final Cut Pro. Whether you are working with sound effects or music, FCP wants a 16-bit 48kHz .aiff file. If you are stuck using an .mp3, you can convert to the proper format in iTunes, however, the conversion doesn’t increase sound quality, it simply converts to a format that makes FCP happy. If you’re lucky enough to have real CD (not a burned one that probably has .mp3s) you can also use iTunes to convert those files (CDs are usually 16-bit 44.1KHz).
While you’re in iTunes, go to iTunes > Preferences. This brings up the Preferences dialog box
Make sure you are in the General pane and click on import settings. This brings up another dialog box.
Change everything to what you see here, then click OK in all the dialog boxes:
Go to your iTunes library, locate the song, then RightClick > Create AIFF Version. This will create a new file in your iTunes Music Library folder.
If you’re importing music from a CD, it will be converted to 16-bit 48KHz .aiff while importing.