Flights are most likely going to be your biggest expense for this trip.
If you are flying from Los Angeles, EL-AL Israeli Airlines is the only airline that has direct flights. Sadly they are also the priciest ones. If you are willing to invest more for comfort, EL-AL will have direct flights from almost any major city. Many other airlines have easy connections. Take in consideration, flying back to the US - connection within the US will require you pick up your luggage and check in again for your connecting flight. The process is quite streamlined, but just something to keep in mind.
Otherwise, we tend to have the most luck booking through google flight search. Sometimes you can find cheaper deals through websites like Kiwi. Just make sure each direction is booked through the same airline in case there is an issue with one of the connecting flights.
* Don't forget to check benefits through your credit cards. We got major discounts booking through our credit card benifits.