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/pLIoov
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.