I'd use a travel bag for each of them. They make ones that you can use, check BRU or onestepahead.com
FWIW, I prefer to gate check them both rather than check them b/c I worry about the car seat getting broken...happened to my friend and she didn't even notice for a while but when she went to wash the cover of the seat the foam piece was broken in half.
Just got back from a cross country trip. I gate checked the two pieces of my travel system without a cover and they were just fine. (Four times total on the trip due to two layovers.)
Re: checking car seat and stroller?
I'd use a travel bag for each of them. They make ones that you can use, check BRU or onestepahead.com
FWIW, I prefer to gate check them both rather than check them b/c I worry about the car seat getting broken...happened to my friend and she didn't even notice for a while but when she went to wash the cover of the seat the foam piece was broken in half.