So basically you want to order the records by date ascending (oldest first) and then by order_id ascending (lowest first), and then grab only the first record.
SELECT order_id, date
FROM table
ORDER BY date ASC, order_id ASC
LIMIT 1;
A more complex (but possibly faster because of less sorting) solution would be to select the lowest date into a server-side variable, then select the lowest order_id for that date, and then select the entire record that has this lowesty date and lowest order_id
SELECT @min_date:=MIN(date) FROM table;
SELECT @min_order_id:=MIN(order_id) FROM table WHERE date=@min_date;
SELECT * FROM table WHERE date=@min_date AND order_id = @min_order_id;
Note: run these three queries seperately, and run them over the same database connection.
A forum, a FAQ, what else do you need?