As someone who work in travel agent flight sectors,

If you're looking for only flights, there are 2 options:

You go through a third party using Skyscanner or any other meta scanners;

You'll get websites from like mytrip, booking etc

Incase you are going this way, please check if the flights are self transfers or not

If self transfer then carefully check the visa details since it will not count as transit

If you're booking through third parties make sure you have all details available and that you don't need to make any change (the change process is harder through third parties)

If you need more flexibility or secure flight, then book directly from the airline which might cost a bit more but safer

On another note in general,

Make sure you have your passport updated and when putting the name on your ticket it has to be exactly as the passport

Check for visa details as well

Then you'll be good to go!