How do I synch my iPhone with iTunes and capture all songs and playlists?

I am trying to transfer all my songs and playlists from my iPhone 5c to my new iPhone 6 using iTunes. I don't want to use iCloud.

I've already created a full backup of the iPhone 5c and deleted all info from the iPhone 6 and restored the 5c backup to the 6 phone, however this only captured the more recently purchased and downloaded songs. On my iPhone 5c I have a couple hundred additional songs from burning my older CDs plus 4 playlists I've created over the years of owning several older iPhones. I've lost the iTunes synch that had the original playlists as it went with an old PC I through out a few years ago so at present I do not have an iTunes synch that includes the full library of songs or playlists that are currently only on my iPhone 5.

How do I synch / backup the songs and playlists on my iPhone 5c so that when I either restore or synch with the new iPhone 6 I capture all of my songs and playlists including the 200+ songs captured from my CDs? I'm find with deleting my iPhone 6 again if necessary.