To be efficient, and random, it might be best to have two different queries.
Something like...
SELECT table_id FROM table
Then, in your chosen language, pick a random id, then pull that row's data.
SELECT * FROM table WHERE table_id = $rand_id
But that's not really a good idea if you're expecting to have lots of rows in the table. It would be better if you put some kind of limit on what you randomly select from. For publications, maybe randomly pick from only items posted within the last year.