Welcome to the Apple Support Communities!
I found the following information that may help you transfer your iTunes library from your previous computer to this new one:
You mentioned wanting to sync an older iPod nano with multiple computers. To do so, you may find the following information helpful:
Regarding your previous iTunes / Apple ID account that you lost track of, we have a very helpful tool in attempting to recover that information:
I know that is a lot to hit you with at once, but I hope it was helpful!