I start with water/salt/statrter first, then gradually add the flour once the mixer starts. I have found that if I start with some of the flour already in there, or add a bunch of it too fast at first, that I see lumps. It can take a while for my mixer to smooth these out, and they just make me nervous. I could be wrong, but I also feel that with my mixer the doughs just turn out stretching a little easier with the slow and steady addition of the flour. This might be because the flour has more time to absorb water, almost like doing a autolyse. Like I have mentioned the "problem" with my machine is when I try to get the hydration lower, so the long slow flour adding stage of my mix helps with that. I have a feeling that with your mixer things would be different. Just like I think everyone's oven probably has a different perfect hydration, every mixer probably has a different perfect procedure. This is also a nice excuse to experiment and make more pizza!
Just food for thought here, a friend of mine was invited to watch one of the top Neapolitan pizzerias (known for having great crust even in Naples) make dough. They dumped 90% of the flour in the mixer all at once right at the beginning of the mix. The final 10% was added right at the end just to get the desired consistency.