You need to look on the datasheet of an old 74xx TTL IC to see that its inputs draw 1.6mA maximum when low at 0.4V. Then Ohm's Law calculates the maximum value for a pull-down resistor as 0.4V/1.6mA= 250 ohms.
Its inputs float high by themselves when not connected to anything but you can use a pullup resistor to quickly charge stray capacitance.
The inputs of a Cmos IC are very high resistance. Its datasheets show its leakage current which drops when the temperature increases. I have used resistor values as high as 22M for pullup and pulldown input resistors on CD4xxx and 74HCxxx Cmos ICs.