I'm still deep into Newbie-territory in my pizza making, but so far, I have not needed any sort of mixer other than my hands. My latest experiments have been with the DKM cracker crust, and while he calls for using a food processor to mix all the ingredients, I have had some very acceptable results just using a pastry knife (I think that's what those are called - those things that have a handle, and 5-6 curved blades). I don't have a food processor, and cheap pastry knives are easy to come by.
I suppose if you're trying to make enough dough for a large number of pizzas a mixer could be needed, though. Since I'm just feeding myself and my wife (and birds with leftover dough), working by hand is perfectly fine... and working dough by hand also has a sort of "Zen" quality to it that can be very relaxing.