Small Baseball Scoreboard using 2 to 3 breadboards
Actually, you can very easily verify this yourself:


Per item (1602LCD, 7 segment LCD and LEDs check how many pins you need and what type, like e.g. I2C or SPI for the 1602 LCD). The 7 segment displays can have many or less pins, depending on the 'controller', See the reaction of CrossRoads below.
Count them together. If it fits on the Arduino you want to use OK. The Uno is cheapest, so if it fits on it, you use that, otherwise you can go to the Mega.
As alternative, and you need 'generic pins, called GPIOs' (not SPI/I2C) for some, you can use multiplexers like 74HC595 to reduce the number of GPIOs needed, at the cost of some speed (not critical for your project), and some more programming work.
In some cases you can use a MAX7219 driver IC, see (again) the remark of Crossroads below.