Opera should install it self by default in C:\Program Files (x86)\Opera if you are installing a stable version.
This sounds logical to me. I am not a computer illiterate and have installed Opera on a number of machines including Windows (7, 10) and Linux. I ran into the problem of the defective icon in the Start menu on one of my Windows 10 machines and noticed that on this machine Opera had been installed in the profile directory and NOT in the default Program Files/Opera directory. During installing Opera I remember not choosing the default options in the installer window, but opted for the 'options' (or the button called something like that). As far as I recall I did not indicate a different installation directory, but Opera was not installed in C:\Program Files\Opera, but in the ´profile directory' instead. Maybe I agreed to that option that was offered by the installer, but I did not intentionally choose a installation directory different from the default one.
Regardless, in my experience the issue of the missing Opera icon in the Start menu occurs when Opera has been installed in a directory other than the default C:\Program Files\Opera (or C:\Program Files (x86)\Opera on 64-bit systems), and can be resolved by (re)installing in the default directory.