For installing iTunes on versions of Windows after 6 (Vista/7/8), your user account should be at the Administrator level. To determine that, go to Start button, look for your icon related to your user account, and click on it. This opens a Control Panel window to your user account and you should see your username, your status as "Administrator," or something else ("standard user" or maybe limited user). You may also see "Password protected" if you needed a password to login. (You should always need a password, even if you are the sole user of the machine. Security is sanity.)
When you attempt to install an application, there will be a UAC prompt usually (never disable UAC...it is your friend.)
It should install.