Objects and floor being cut off when zoomed in I've seen tutorials on this site from the old lay out, but even after editing the "Clip Start" setting, when I'm in the 3D Viewport, it still clips.

Can anyone help me find out what I am doing wrong?
You are editing your scene camera's clip settings, when you really need to be editing your view's clip settings.  

Press N to bring up the side menus, go the the "View" tab, and you should find the relevant options.