We are new parents and this is our first time traveling w/our baby. We our flying SW Airlines. They allow us to check our car seat & gate check our stroller. We have luggage destroyed by the airlines & are afraid of checking these items. We have a Chicco car seat & Baby Jogger City Mini stroller. Any suggestions on what we should use to check them? There are actual carrying cases sold by baby jogger & JL childress. Also the big red gate check bags. Do airlines supply bags? Your advice and experiences on airlines would greatly help! We fly out this Saturday 1.5hr flight. thanks