If I sync my Apps on my iTunes, would it save all my game progress?
Just download the my contacts app. It backs up your contacts then emails it to you. Just click on it in your email and it will download all of your contacts to your phone.
This is what I'm wondering or, like someone else mentioned, wouldn't it sync your progress via game center or no?
If my apps are on my iTunes and I set up as new and install the apps from iTunes. Does any data from apps carry over?
Only if you restore from an iTunes backup, or if those apps use iCloud (or another sync service) to keep your data.
With every new iPhone I always just do the restore from iCloud Backup. This year with the iPhone 6 I was thinking about just starting fresh with a clean install. Is there really any benefit of doing this or should I just restore as usual?
I would like to know the same thing! I have actually already restored from backup but I could erase and set up as a new phone. So far it's performing great!