This is my current home screen on my iPad 4. Yes, all my installed apps are in that folder in the top left. I chose the wallpaper specifically. :)
I do a short swipe down on the Earth to find and launch an app. Swipe from the top to see my notifications (no badges, most sounds and temporary banners disabled too.) Swipe from left for weather and other useful stuff.
I left TuneIn Radio in the dock for the simple reasons that a) it's what I use during the night and to wake me up in the morning, and b) you cannot make the dock disappear, and it looks a bit silly just hanging there, completely empty.