Traveling with 3 and 1 yr old to Seoul

Hi! It’s our first time traveling with kiddos and we are feeling quite nervous about it. We are taking a car seat for my 1 yr old and got a CARES strap for my 3 year old. We are taking a stroller that is foldable to fit into a cabin. I’m hoping to use the stroller for my toddler and wear my 1 year old during the trip.

My question is how many luggages should we take? Should we get a car seat backpack or a strep that goes around your carry on? I don’t want to take too much and feel overwhelmed by kids and stuff. We will be taking lots of public transportations and going to jeju and busan which only allows 15kg luggage and a carryon. Any advice?