You have two iPhones now right?
The new one if you click set up as new it will just let you start using iTunes without doing anything. After you do that you can unplug the new one and plug the old one in and backup the info to iTunes.
If you still want your contacts and stuff then go to setting and sync your contacts to iCloud or any email that you want. If you do that then all you need to do sign in to that iCloud or email account on the new phone and get the contacts back.
Hope this helps!