I just purchased a new iMac. I want to know how to transfer my old bookmarks from my old iMac running High Sierra to my new iMac running Catalina.
If you're just wanting to transfer your Safari Bookmarks, then:
In Safari, on your old Mac, you can export the bookmarks, Safari > File > Export Bookmarks… and you can then import them on your new Mac using, Safari > File > Import Bookmarks….
Note: In macOS High Sierra the Safari bookmarks are stored in ~/Library/Safari/Bookmarks.plist. You can copy the file to the same location, with Safari closed, on your new Mac if you do not have any bookmarks yet.