Why can't you connect with the App Store? Error message(s)? If you boot into another admin account, can you connect?
Check the computer requirements shown in each link to see if your computer is capable of running that OS version.
How to upgrade to macOS Mojave - Apple Support
How to get macOS High Sierra
Sierra download
You can try to download it at the link below. If it won't let you, then your only options are to upgrade to Sierra/High Sierra/Mojave or find an older computer where you can download it using your Apple ID.
El Capitan
Check to make sure your applications are compatible. .
Application Compatibility
El Capitan 10.11 Compatibility information
macOS Sierra 10.12: Compatible Apps
Also check to make sure there is a compatible driver for your printer.
Do a backup before installing, preferable 2 backups on 2 different drives.