Traveling internationally and domestic

dimple
Hi,
I am planning on traveling both domestic and internationally when my son turns 5 months and I was wondering if you have any advice about purchasing a seat for the baby vs keeping them on your lap.
Also, any advice on carrying a car seat, car base and stroller? Do most airlines check this in for free? Do you have to pack the base in your checked luggage?
Any advice would be helpful.
Thank you