To turn push notifications off completely, just turn off everything you just listed for that particular app: badges, banners, sounds, and whether the app appears in the 'notification center'.
Please keep in mind that this is iOS, not Android. Meaning that not every app has to keep a connection open to some server, but there is *one* central connection that is kept alive for *all* push notifications for all apps.
In other words: if you turn push off for an app that doesn't receive any, there will be no change in battery life whatsoever. The easy way to know which push notifications are sucking your battery life, just look at what you're receiving more often during the day. If you receive a facebook notification every 5 minutes, all day long, the screen will always have to turn itself on to show it to you. This adds up usage minutes and uses battery.