Sparkfun sells 4 digit, 7-segment displays that have a simple serial interface (serial.print("1234");). They are four digit so not perfect for your need for 2 digit score and 1 digit period, but with a cleverly set up scoreboard you could overlay the third digit of one display and functionally split it into the home score and period, and another display would leave two digits uncovered for the visitor score. A third display would be used for the time of course.
That does amount to $39 for the displays but they are very easy to use.
If you want to build it from discrete components then the most straightforward method is to use one shift register with each 7-segment LED. The wiring and programming gets much more complicated, as you can see.