I’m probably not the best person to ask since I just drag stuff from folders on my computer to folders on my MP3 player.
Exaile is the default Xubuntu media player and I actually like it a lot. It’s light but simple. I can’t get it to burn CDs, but that’s not too horrible.
In the past, I’ve used the underrated Goggles for music management.
Both of those are fairly basic tools, though. If you want something with the sweeping grandeur of iTunes (but stable and responsive, unlike iTunes), the big guns are Rhythmbox, Banshee, and Amarok.
I’ve used all three at one time or another and I couldn’t tell you the difference between any of them. Luckily, Linux Journal did a nice roundup a few months ago.
Play with some and see how they work for you. And let me know which one you end up sticking with.