I find Google Flights to be the easiest way to research flights, independent of hotels and package options. You may end up with different airlines, which may require booking on separate websites, or on one discount site.
Momondo is another great site for researching flights and can be used to cross-check Google Flights.
Credit Card Services
Your credit card may provide travel booking services, or if using card points. Once you find the flights you want, you may call them to help you book more complex itineraries.
You can fly private at a discount if you happen to be traveling where seats need to be filled. Try these sites for a first class adventure!