Working on a project that will list12-15 business support

Hi Guys,
Working on a project that will list12-15 business support groups.
I have them in a category page in the top/main menu.

I've tried listing them in alphabetical order using post order plugins and I seem to be having issues. The plugins work great in the back end, order just fine. But the order is not translated to the front end of my theme.
If I can't resolve this, which I pretty much given up,
then I would like to find a cool way to list my category posts on this page.

Is there a way to rotate the list order so each time the page is refreshed it comes up sith a different list order for the same category posts?
That would be cool and keep interest.

Thanks for all the help.
Richard