Darlington Transistors ULN2003APG Base Voltage
Per TOSHIBA's ULN2003APG datasheet, this driver already has built-in input base resistor, for ULN2003APG, the resistance is 2.7k\$\Omega\$. It's dedicated to interface directly to TTL. or 5V CMOS level. So you can directly connect their inputs to your MCU.

For driving LEDs, the common pin maybe left open.

Because it's a sink (not source) driver, so you can connect your LEDs with anode tied to power supply, and cathode with a current limiting series resistor to the driver's output pin.