Preheat the oven to 450° and bring a large pot of salted water to a boil. Add the ziti to the pot and boil until just al dente. Drain and return the ziti to the pot.
Meanwhile, in a large, deep skillet, heat the olive oil. Add the onion and garlic, cover and cook until just softened, about 2 minutes. Add the ground sirloin, crushed red pepper and paprika and season with salt. Cook over high heat, stirring to break up the meat with a spoon, until the meat is no longer pink, about 3 minutes. Add the marinara sauce and bring to a boil. Cover partially and cook over moderate heat for 5 minutes.
Add the sauce to the ziti in the pot and stir to coat it thoroughly. Add the ricotta in large dollops and stir gently, leaving it in large clumps. Pour half of the ziti into a 9-by-13-inch baking dish and top with half of the mozzarella and Parmigiano. Repeat with the remaining ziti and cheeses.
Bake the ziti on the top rack of the oven for about 15 minutes, until it is bubbling and browned. Let the ziti rest for 10 minutes before serving.