Now here's a loaded question that will get a number of different answers...and the great (and confusing) thing is that none of them are wrong!
Thin crust: Aurelio's (Homewood), Home Run Inn (Cicero, daytime is much safer), Vito & Nick's (on Pulaski, SW side near Midway Airport) are great starting places, but there are SO many others.
Deep Dish/stuffed: Critically, it seems that Lou Malnatti's/Pizano's seem to be the most in favor, but those along with the rest of the bigs (the orig Uno/Due, Giordano's, Gino's East, Bacino's) all have their merits. About 5 years ago, the Chicago Tribune did a taste-off of 100+ places, and the winner was a place just north of downtown calld The Art of Pizza.
By the way, you can even find some good deep dish pizzas here in SoCal! Have a great trip!