Airlines
This option is the most straightforward. Booking directly through the airline means you will only fly on that airline or their partners. Tends to be the quickest.
Pros:
Will provide the most simple itinerary.
Changes to your itinerary (cancelations, delays, etc…) will be easier to mitigate since your ticket was booked directly through the airline.
You will rarely need to recheck your checked baggage during a layover.
Quite often the quickest way to get to your destination.
Cons:
Typically a more expensive option.
Your destinations are limited to wherever the specific airline or their partners fly.