How do I correctly go about syncing my iPod touch to a new library?

Hi, I have a 3rd generation iPod Touch. Back in 2009, I synced it up to a pretty old computer. At the time, the newest version of iTunes worked perfectly on it. But since a few months after that, my computer was not able to support the most current version of iTunes available at the time. After a while of trial and error, I gave up on syncing my iPod Touch to the computer. But now, I have ordered a 5th generation iPod touch, and would like to transfer what was on my old iPod, to it. I do have a different (and newer) computer that I am now wanting to sync up both iPods to, so they could share information. I'm thinking I need to re-sync my old iPod to my old computer and transfer all the new apps, songs, and what not. But I'm not sure what to exactly do after that. If syncing to a new library only erases songs and video, I could put them on a USB and download them to my new computer. So when I sync my old iPod to the new computer, the erased data would be already there. And I could just re- download it. The main problem with my theory is, I'm not sure what syncing to a new library actually does to an iPod Touch, or any iPod for that matter. I've been anxious about this, since my iPod Touch is very important to me. I've been using it almost everyday since I first received it. Any help on this would would be greatly appreciated. Thanks so much!! 🙂 🙂

-Becca