Should you drink wine or beer with pizza? No rights or wrongs, obviously but here are a few thoughts which might encourage you to experiment.
Italians themselves more commonly drink beer than wine, usually a light lager like Peroni Nastro Azzurro but I personally like something with a bit more flavour - a Czech lager like Budweiser Budvar for example or, with spicy pepperoni toppings, a Viennese-style lager like Brooklyn.
Inexpensive Italian reds are also ideal being moderate in alcohol and with the fresh acidity to cut through gooey cheese and tomato toppings. I personally enjoy Chianti with pizza but you could equally well drink something like a Barbera, a Valpolicella or a Rosso di Montalcino or a simple Sicilian red*. Italian grape varieties such as Sangiovese and Dolcetto made elsewhere in the world also work well but you might want to chill them lightly to offset the extra ripeness and sweetness.
Other good pairings would be a fresh-tasting, medium bodied red like a Merlot, a Syrah, an inexpensive Zinfandel or a young Rioja.
There are also times when I think white wine works better with pizza than a red. Examples include goats’ cheese and spinach pizza, pizzas topped with prawns or other seafood and pizza bianco (without tomato). Again Italian wines seem to hit the spot perfectly, even the ubiquitous Pinot Grigio, though other crisp dry Italian whites would be equally good. I also enjoyed cider with a seafood pizza recently - no reason why not.
And with pizza topped with with fresh ingredients such as parma ham and rocket? Try a dry Italian white like Gavi or a well-chilled glass of prosecco!
*Another good suggestion (from @lauraloveswines) would be an authentic dry red Lambrusco or a Bonarda frizzante.