If you are wanting a single screen with access to all of your apps... I'm not sure there is a way to that. iOS provides three ways of opening an app: springboard, spotlight, and Siri. Springboard is pretty good, and when combined with folders you can store quite a lot on just the first page.
I am not aware of a UI idiom that would provide access in a way you imply.
I'd like a single folder for each application type, then an alphabetical list of apps - maybe working something like the contact list. As it is I am stuck with dozens of folders (for each letter of the alphabet, and because of 12 app per folder limit, I have four "Games S" folders.
I am not aware of a UI idiom that would provide access in a way you imply.