With the iPhone to transfer computers , you can transfer all the old content first computer , then transfer to your new iPhone.Here is how to transfer iPhone to iPhone . First transfer content to your PC with iPhone, iPhone to PC Transfer. Then add content to iTunes and sync with another iPhone. Hopefully it can help.
I can't say it enough...authorize more than one system so you can house your backups in more than one place. If your initial system breaks down then you will have a back up for that. If you are using a Mac then you can use the time machine...hopefully.