The best way is to use iTunes or iCloud. Follow these steps to back up your previous device and then restore the backup to your newly purchased device. Your saved messages, email accounts, photos, notes, and other personal settings will be transferred to your new device.
The only way to get itunes content on your new phone is by syncing or manually managing songs & videos through itunes. You can sync as many devices as you want to the same itunes account, there is no limit with a software like this: http://goo.gl/QyVOfB
Unless you created playlists(smart idea), then you have no choice but to go through itunes & select the content you want on your new phone or if you have checked "Sync only checked songs & videos". From your post I'm guessing you have "manually manage music & videos" checked, correct? If so, you should be aware of the fact that there is absolutely no advantage to doing so with an iphone. Unlike disk wheel ipods, the iphone does not support disk mode. Thus, you're better off creating playlists & syncing those to your phone.
The iStonsoft iPad/iPhone/iPod to Computer Transfer could help you do so but it still need to use a computer. If you don't mind that, you could download the free trial version of this software to have a try.
How to copy or move songs from old iPhone 3GS/4/4 S to a new iPhone 5/ 5 C/ 5S? And for an easier and faster solution, iPubsoft iPad/iPhone/iPod to Computer Transfer is highly recommended. Why not give it a trial? http://x.co/40IbC