I am finishing a basement 3/4 bath. I have run a separate 20 amp (12g) circuit from panel to GFI outlet in bathroom. From that I want to run to bathroom fan.

Can I run to fan and then to switch for the fan or do I HAVE to run the wire to the switch and then the fan - I have been told I must go to the switch first from a GFI... I don't understand why this would be true.

I want to run the wire from the GFI because that is on 12 gauge wire and that is the only 12 gauge/20 amp circuit in the bath. I have not purchased the fan yet but want to be prepared assuming it calls for 20 amp.

Please help.

Unless Manufacturer reccomends, Usually you don't.
I would run power to switch location, then to 3 locations(the GFI, The Light, and the fan)

In order to get the maximum benefit from the GFI, you MUST run the power to the GFI first, then to the switches, and from there to the fan, lights, etc. That way, the lights, fan, switch, and GFI will all be protected from a ground fault. Otherwise, only the GFI itself will be protected.

Carefully read the installation instructions that came with the GFI. It should explain why.

I don't see any need for GFI protection of the bathroom light and exhaust fan, unless either are directly over the tub or shower enclosure. If the GFI trips, the bathroom will be dark.