Do I need to connect a resistor to either one of the 2 input pins of this "and" logic component? If so, what would be the value for it?
No resistor is needed, just make sure whatever voltages are presented to the input pins are either between 0 and the maximum voltage for a logic 0, or between the minimum voltage for a logic 1 and the supply voltage.

The maximum voltage for a logic 0 (3*VCC for a supply voltage between 4.5V and 5.5V), and the minimum voltage for a logic 1 (0.7*VCC for a supply voltage between 4.5V and 5.5V) will be in the datasheet.