Yes Best buy can transfer your music for you. You will need to contact the store as I am not sure as to what they charge. And yes best buy has a trade in program. You can get a estimate of what you could possibly get here.
You'll need to copy everything from the old iPod to an iTunes library first before you can sync it to the iPod unless the music on the older iPod already stored in an iTunes library. In that case, just connect the new iPod and let it sync whatever content you desire.