Dimmers & fans will absolutely not trip a GFCI inadvertently. I do recommend using one GFCI recept, not more on the same circuit. The other recepts can be regular and attached to the load side of the GFCI one and will inherit the protection. All my bathrooms lighting is on dimmers, the fan is on a timer, and all are on the load side of my GFCI (protected) and have never tripped.
There's basically 2 methods for wiring a bathroom by code...
Here's your choices
1.) All the recepts of bathrooms can share the same 20A GFCI protected circuit. Lights & other stuff go on another circuit. Since all the recepts of the bathrooms share the same circuit the breaker will trip if 2 people use a hair dryer at the same time in different bathrooms but since lighting is on a different circuit they won't be left in the dark. I find this useful when there's a small master bathroom with a regular bathroom on other side of the wall. Just one 20A circuit to a GFCI recept and the rest of the recepts of both bathrooms attached to it and requirements are met. Lighting goes on a general circuit (or shared).
or when remodelling an older house often one finds the bathroom is on a 15A general circuit (using #14). To bring it up to snuff it's easier to just let the lighting and #14 remain and run a new #12 line to a GFCI recept in the bathroom, add a 20A breaker and call it a day.
2.) Or all the stuff in the bathroom can be tied into the same dedicated 20A circuit (the way you mentioned) using at least #12 size wire for the whole thing. The recepts have to be GFCI protected anyway (since NEC 1975) which adds nothing to the cost if you want to have your other stuff protected as well. You can have all the lights/fans/dimmers on the load side of the GFCI recept making them protected OR not. It's your decision but all recepts must be protected. Some situations require lighting/fans be on GFCI (over a shower usually), but lighting attached to the load side will shut off if the GFCI trips and some argue being in the shower with no lights is more dangerous than protecting the lights with GFCI so they opt not to. However, I personally like having the total bathroom protected especially with a kid. So far, can't say one way or the other my GFCI has never tripped.