Pour olive oil into a 5- to 6-quart pan over medium-high heat; when hot, add onion and garlic and stir often until onion is limp, 3 to 5 minutes. Add wine, tomatoes (with their juice if canned), tomato paste, basil, and pepper; bring mixture to a boil over high heat, then reduce heat and simmer, stirring often, for 10 minutes. Add salt to taste.
Meanwhile, rinse and drain fish, shrimp, scallops, and crab; cut fish into 1- to 2-inch pieces. Scrub clams. Gently stir fish, shrimp, scallops, and clams into tomato broth; cover and simmer just until fish, shrimp, and scallops are opaque but still moist-looking in center of thickest part (cut to test) and clams have popped open, 7 to 9 minutes. Discard any clams that don't open. Add crab and press gently to immerse in broth; cover and cook just until hot, 2 to 3 minutes.
Ladle cioppino into wide bowls and sprinkle with parsley. Serve with bread and lemon wedges.