How should an index page be setup/defined in Craft?
Depending on the rest of your site structure, yes you can set these up as Singles.

Your other option is to use an Entry Type inside a 'pages' Structure, and in that template you list the first 6 categories in a defined Category Group (possibly selected in a dropdown, or through craft.request.segment() )

Documentation link on how Craft looks for index templates in case it's useful: https://docs.craftcms.com/v3/templates.html#index-templates.