I suggest you search for flights on kayak.com, using the "multi-city" option. I did a search for LAX-Venice and Rome-LAX on random October dates and found several flights on Delta, Alitalia, and other airlines (many involving code-sharing). There are several nonstops between LAX and Rome. Venice requires changes at places like JFK, Amsterdam, Paris, Rome, and others. Try to stay with one airline if possible (including code sharing) so you'll be on one ticket, guaranteeing a later flight in case of delays enroute. If you have a layover, especially after a long flight that might be delayed, try to make it at least two or three hours. I like to fly to a European airport first (from Seattle), so if I miss a connection at least I'm on the right continent with multiple options.
When you've found the flights you like, schedule-wise and price-wise, book them on the airline's own website (which should also have a multi-city option). That will make things easier if you need to change plans later, including a missed connection.
EDIT -- Flying into Venice may be a better idea than flying out of Venice, simply because Venice is an island and the airport is on the mainland. Depending on where your hotel is, you may have to take a boat part of the way. Weather and other uncertainties of water travel might complicate getting to the airport, risking a missed flight. Getting from the airport to the city doesn't involve the same time pressure.