It is good practice to always add series resistor, like in circuit 1. The only exception is if you drive very small fets with very low gate capacitance. Calculate series resistor based on maximum permissible pin current. For example, if voltage is 5V and maximum pin current is 20mA, use at least 250 Ohms series resistor.
For logic ICs, MCUs and other fast switching ICs, capacitive load presents almost a short circuit to ground during fast transitions. So for a brief moment current might hugely exceed maximum limits. Although it's very short and usually does not present significantly increased thermal dissipation, high current peaks might cause momentary sag of supply voltage, either for the whole IC or some section of the IC. Especially if IC does not have very good bypassing. And in general stresses the ouput of IC without reason. If you want to drive a mosfet gate fast, you use some sort of dedicated driver.
FYI, power mosfets typically have 1-10nF gate capacitance, that is significant.
The need of gate pull-down resistor depends on the application. It is good practice to add it, except if you are sure that driving pin can never be high-z, aka floating.