The easiest way is just to use your database to select a random row every time. In MySQL, it's something like:
SELECT * FROM table_name ORDER BY RAND( ) LIMIT 1
If you really need to cycle through every row in order, then there are different ways you could do it; maybe add an extra row at the beginning of the table that keeps track of which row you selected last, then use that information every time you select a new row from the table and increment the counter.
Of course, you'd have to use PHP to make sure the counter wraps round properly, so it's really easier just to use random selection: it spreads things fairly evenly, so you shouldn't have any problems.