Book as many legs of the trip as possible on a single ticket, and with the same airline and its partners if you can. That approach eases booking, luggage transfers, and possibly price. You may have to design any layovers yourself by putting the dates into whatever search page you are using. To see if it can be done without raising the price, simply run a test. Airline policies vary on adding extra time to a stopover.
Of course non-stop flights are the easiest but not necessarily the cheapest. In general, changing planes in Europe will probably be less stressful than in New York, although Paris Charles de Gaulle can kink up anyone's patience. I find Atlanta a pretty comfortable airport for transfers too.
To get a better idea of airline routes, look at www.itasoftware.com. It provides info for many (not all) airlines although it doesn't sell tickets.

I am traveling to Italy from Houston and am looking for an airline that has flat bed seats for the long flight. I have looked into Air France but have heard that they go on strike quite often. Any suggestions?

As to San Diego to Venice, I would avoid a layover in London. It is expensive to get from any London airport into the city and back, and lodging in London is quite expensive. If you still want to do it, use the multiple destination option when you are looking for a flight with San Diego to London as your first leg, London to Venice as your second, and Venice to San Diego as your third, then compare that cost to the cost of a flight without the layover. If you are really frugal, and have almost no luggage, you could consider a low cost European airline, such as Ryan Air, for the middle leg. Your multiple destination ticket would then be San Diego to London, and Venice to San Diego.

As to lie flat seats, I have never seen one in the tourist class section, so you have to buy business or first. Many airlines have them, but a few don't yet, and last year I flew on a United flight that was supposed to have them but didn't. To be as certain as you can, find a flight and copy down the models of the aircraft they plan on using, then go to their section on inflight amenities and find a list of their planes. Each type of plane should have a chart showing the type of seats. Be careful of terminology; some airlines use words like full recline to trick you into thinking it is a lie flat seat. There is a website http://www.seatguru.com/ that has pretty accurate information also.

Try looking at flights to Bologna or Milan. They are sometimes less money.

Try http://matrix.itasoftware.com/ or kayak.com.

Thank you everyone for your input. This was very helpful. I will keeping working the options.