Doing numbering is extremely easy in the Advanced Rename Dialog. Don't be put off by the dialog's name. Give it a try and you might learn something.
There is a short page on how to use it to number files here:
https://www.gpsoft.com.au/help/opus12/index.html#!Documents/Numbering_Files.htm
Random numbering is also possible via a rename script. You can load that into the dialog and it will then also be available via the menu off the Rename button on the default toolbars. Here is the script: Add a Unique Number while renaming
Alternatively, for another way to get the files in random order, you could use Button: Random Shuffle which shuffles the files in the file display, and then rename them numerically (without any extra script) to keep them in that order when they are sorted normally by name.