What is the best way to forward my NC State Gmail to a non-NC State e-mail address?
Before forwarding your Google Apps @ NC State Gmail to your personal Gmail in particular, consider that it might be nice to keep your NC State Gmail separate from your personal Gmail. For example, if you keep them separate, when sharing a Google Doc with a classmate, you can share it to your UnityID@ncsu.edu Gmail address instead of having to give them your personal Gmail address to which to share it.
If you do want to set up forwarding, see Google's Forwarding mail to another email account automatically procedure.
If you previously created server-side filters (also called "Sieve filters") in Unity/Webmail to forward your mail, or to do other things such as automatically move messages upon arrival into certain folders, you will need to recreate them using Gmail filters.