About This Mac will be correct. Look in your Applications folder for Install macOS High Sierra.app if it is about 5.23 Gbs then the download has completed, you can double-click it to start the installation procedure. First it is recommended to make a copy of the install app prior to installing, put it on an external drive or USB stick as the one in the Applications folder self deletes after installing. This negates having to download it again should anything go wrong in the future.
As you are upgrading from Mavericks make sure any third party apps you use have updates available so you can continue to use them in the new OS. also check that any printers/ scanners etc have drivers and software available so they don't become obsolete under High Sierra.