You can just make a pool for the week make the order random on that week and then reset it the next week. Then you make sure that atleast the character wil appear once during the week and doesn't get repeated. If there are less character you can make a condition that it can repeat a character one time by checking how many times that character got repeated into the pool.
This method assures you a random style of characters but assuring that you will see the character you like at least once