Iphone 6 won't connect or download from appstore

My 'new' (a couple of weeks old) iPhone 6 wouldn't download a free app from the store. I tried closing app store, didn't work. I tried logging out of the app store under "Settings" -> "iTunes & App Store" and now it won't even let me log in again! I've tried both on and off the wifi at home, I have 4G on my phone that works when I go to google, but I still can't log in. What do I do? My iPhone is 'ajour', I checked that before I logged out of my apple-ID.