Go to Options, General tab, and in the box marked “Run these commands every time Rhino starts” put the following:
!_SetDisplayMode Viewport=All Mode=Shaded
This will work if you start Rhino by picking a file from a directory list, but not if rhino is already running and you use the Open (file) command, because in that case the new file overwrites the display settings when it opens. (Rhino is already started in that case, so it will not run the command from the General Options.) It also will not work if you pick a file from the startup splash screen, because when you do that Rhino starts first and then opens the file.
This will work if your default template file is still wireframe so you don’t have to modify it as Sam mentioned, but there are lots of other reasons to fine tune your default template (custom materials palette if you use the same materials often, for instance), so I would do that also.