Re-wiring a bathroom
The easiest thing to do, would be to wire it up like this.


Grounding conductors excluded for simplicity. Make sure the grounding conductors are connected properly.


Install a 20 ampere breaker in the panel.
Run 12/2 with ground from the panel to the switch box.
Run 12/2 with ground from the switch box to the fan, and the light.
Connect the black ungrounded conductor to the two switches and GFCI receptacle, using pigtails.
Connect the white grounded conductor to the GFCI receptacle, and whites from the cables running to the fan and light.
Connect the black from the fan cable to one switch.
Connect the black from the light cable to the other switch.
Connect all grounding conductors.