The gate resistor should be high enough to limit the peak current on the AVR's pin to about 30-ish mA. Consult the datasheet. I think for some AVR chips, the absolute maximum is 40mA for GPIO pins.
So 160Ohm would work for 5V.
Using the GS-capacitance, you can calculate the RC-time and see how long it takes for V(GS) to be reasonably high for the mosfet to turn on fully. That will also give you the upper limit for the PWM frequency.
For really fast switching you need a mosfet-driver ic, that can charge the gate really fast and avoid thermal loss in the transistion from off to on.
The pull-down resistor (bleeder) is not that critical. If you like to conserve power, 10k seems a bit low. Again, calculate the RC-time if you think it matters.