Do you want to be standing in the dark when the GFCI trips?
Wire the lights on the LINE side of the GFCI.

Hook the light and fan to the line side of the GFCI. Neither one needs to be on the GFCI unless they are in the tub/shower enclosure area, and it's never a good idea to have a GFCI trip and put you in the dark. Personally, I'd run the new circuit to the GFCI and tap a lighting circuit from another room for the light and fan.

You're right about tripping GFCI and darkness...don't want to go there. I was just thinking about how a hair dryer plugged into the GFCI would possibly dim bathroom lights if everything was on the same circuit. I'll do a dedicated circuit to the GFCI and tap another light circuit for fan and lights.
Thanks

If the fan or light is over a tub/shower, the manufacturer may require them to be GFCI protected. In my bathroom, the light over the vanity is on the line side of the GFCI and the light/fan over the tub is on the load side.