Google Flights first, and then I go to the airline's site to purchase. I never deal with third-party resellers - they might be cheaper in some cases but a nightmare to deal with if the flight changes or gets canceled.

I like Google Flights so much that I also built a Chrome extension[1] to improve the interface (hiding the third-party affiliate links, putting seat data in the top-level of the results, and making business class searches easier).

[1] https://chromewebstore.google.com/detail/skysavvy-enhance-go...