Trying to update OS from Yosemite after recovering

iMAC crashed. I reinstalled and went to an old Time Machine Backup. The problem is that the MAC OS is Yosemite. It doesn't seem to play well with other applications, won't go to support.apple.com because Safari can't establish a secure connection, and it doesn't give me any options to upgrade the OS in the App Store.

I went to download the install program for High Sierra from this laptop onto a thumb drive so that I could bring it to the iMAC. But the webpage cautions to only use this to install over a slightly earlier version of High Sierra. So, I'm out of luck it seems. Help, please.