I know about pizza around the East Side...
+Zaffiro's (Farwell between Royall & Brady) is legendary for thin-crust pizza in a very non-fancy atmosphere. They don't deliver, but stting at the bar to wait for a pie is part of the experience. They're cheap, too.
+Pizza Man (corner of North & Oakland) does great pizza, too. Try the one with artichokes & cream cheese. They deliver.
+Palermo Villa (Murray Pl. near North Ave.) does okay, too.
Pizza Shuttle & Zayna's aren't great. I still order from them sometimes when I need it cheap, fast and lots of it.
I've also heard great things about Maria's on Forest Home somewhere. From the outside it looks grand, with old neon & signage, and friends claim it rivals Zaffiro's for cracker-thin crust and fresh toppings.
I'm not a huge fan of deep-dish pizza. I only know the chain places that have it - like Edwardo's and Pizzeria Uno.
Good luck! Tell me if you try any of my suggestions.