Will your flight booking API give me the low cost airlines as well, or only the big network carriers?

Yes, low cost airlines can come through the flight booking API alongside the big network carriers, but exactly which ones appear for you depends on the suppliers connected to your account and the plan you are on.

Low cost carriers usually reach you through a different source than traditional airline fares, so they can behave differently in the results. The fare you see is often the bare seat only, with bags, seats and meals offered as paid extras afterwards. Many of these fares have to be paid at the time of booking rather than held, and the ticket rules tend to be tighter, so a change or a refund may cost more than your customer expects or may not be possible at all.

I should be honest that no single connection reaches every low cost airline in every market. Some of these airlines sell only on their own website, some ask agencies to sign a direct agreement before they will release fares, and a few appear in search but cannot be ticketed automatically. Where that is the case you would still need to book directly with the airline and then record it in your account so your reporting stays complete.

The simplest next step is to send over the routes and the airlines your customers ask for most often, so the available content can be checked against them before you commit, and then run a few of those exact searches in the test environment to see what actually comes back.