How can I re-set “Safari” as my default browser.

gale lea wrote: "I cannot get Safari back...frequently Safari cannot find the server"

iOS/iPad

1. Section: Delete history, cache, and cookies

https://support.apple.com/en-us/HT201265

2. Section/point 7: Still can’t connect

https://support.apple.com/en-us/HT204051

See this article macOS Sierra: General System Preferences

Click on drop down arrow and choose as safari .If you are using different web browser say chrome or any and wish to switch to safari you have to log out from chrome account then open system preferences > General and manually change it then in safari preferences > General you have to set home page using search engine as google or whatever ( delete the old search engine in home page and add a new search engine manually or open a new tab ( command and T ) open google link and copy the link and paste in previous tab home page field , you can see this article Set your homepage in Safari on Mac - Apple Support

Do you use any application like Chrome or Gmail?

When I enter settings to Safari,to search engine, google is selected, safari is no longer on the list to select,

Safari is a browser, not a search engine.

Go into your safari preferences under general. The top line is set safari as your default click on that and that should work.

and btw again Safari is a browser not a search engine