Whenever I update my iPod, itunes on my PC wants me to restore?

I have an iPod 5G, which I use with iTunes on my Windows PC. However, whenever I update my iPod (in this case, to iOS 9.0.2), iTunes no longer syncs with my iPod, and requires that it restore before it will sync. I have previously restored for this exact reason, and had to go to the nearest iTunes store to take it out of recovery mode. Though this worked, it seems like a large hassle, so I was wondering if: A. there is a way to prevent this from happening every time I update, and/or B. what is the "correct" way to put an iPod into recovery mode, restore it, and take it out again? The employee who helped me said that I had to release the home button and press it again to restart the iPod, but I don't want to have to put it into recovery mode without being 100% sure I can take it out again on my own.

I have tried removing the iTunes application on my laptop, then re-downloading it. Both iTunes on my laptop and the software on my iPod are up to date.

This is the message I get when I plug my iPod into my computer:

And this is how it appears in iTunes:

Sorry for the length, and thank you in advance.