Changing my Iphone and using ICloud?

So I have an Iphone 5 and I'm planning on changing it for a new one because I think the sensor thing is not working well. If I get a new one with the guarantee, how do I use I cloud so that all of my apps and pictures will be on the new iphone. I don't have photo stream on because I don't want my pictures going on other devices with my icloud username. And I have the app: photo vault which keeps pictures " hidden" by requiring a password to see them, so how will I ensure to know all of these secret photos and apps and pictures with no photo stream on will be on the new phone?

You can go to http://www.icloud.com/...icloud.com and it will show you what files you have backed up.