Travel as slightly as you can is my advice.
As as a veteran of 5-6 long haul returns from the age of 6 months to 20 months, we quickly realized the benefit of taking as little as possible, esp through security.
We we went from buggy bags and full parafanalia to just using a couple of bungees to keep the two parts of the buggy together and a single small bag for the kid within two trips.
Deffo check the car seat and buggy and carry the baby while he/ she is young/ small enough to do so, they're just a nuisance at multiple occasions beyond check in