Best sites to search for flights
Kiwi.com, former Skypicker
I started using Skypicker, now Kiwi, pretty much the moment they launched a few years back. Compared to some other websites, you can search for multi-leg flights, combining numerous different airlines, and buy the ticket from them through Kiwi. When I last booked with them, I remember it was Ryanair's flight, and they even did the checkins for me. Not to mention the fact that I didn't see any of the annoying Ryanair ads. Their service fee, if it hasn't changed, is usually anywhere from 5-10% of the original flight cost.
The main bonus for me when it comes to Kiwi, is that you can actually search for flights from numerous different cities (using the radius search) to numerous different cities during the next 30 days for example. Which means that you can really find the best options for you, especially if you don't have any set dates when you need to travel on.
For example, right now I just made a random search, in two weeks I could get a flight from Riga to Bangkok, via Kiev, for EUR 213. And the entire journey takes just 12 hours.
The main thing about Kiwi is that it really gives you great broad search options.
Momondo has lately been my favorite. It's fast, straightforward, it includes the chance to include nearby airports and might include flights where you need to move from my airport to another. All in all, if you're looking for something for specific dates, using Momondo is the best idea.
Everything else - you can use them, but Kiwi and Momondo usually get the job done.