Whether in a car seat or not, bring something the baby can chew on for the 1st 20 minutes into the flight and the last 30 minutes of the flight - babies ears don't adjust well to the pressure difference, and they need to be sucking/chewing to make up for it. Whether the plan is for mom to nurse, baby to take a bottle, baby to chew on a toy, baby to chew on a pacifier, etc, having something that the baby will always happily chew/suck on is the most important thing for you and baby to have a happy flight.
Also, always bring a spare outfit change (for you and baby) and extra diapers and wipes - a wet, dirty baby is an unhappy one and you'd be amazed how much life is better with this (see below).
Always bring some food source and beverage source (even if it's an empty sippy cup you fill post security).
Always bring 2-3 toys/books for entertainment - don't rely on the phone (except as last resort) b/c it's more annoying for people to hear different videos every 5 seconds than a nicely read book from mom and dad and babies won't wear headphones.
I always flew with all of mine on a lap (even internationally) - I had one motion sick one, so the car seat would have been a disaster 20 minutes into the flight (keeping her upright and able to view a sight line was very helpful to keeping her stomach settled since she was too young for Dramamine, although we still lost her breakfast on an international landing once...at least we were getting off the plane to see daddy to clean her up (while I changed)...it was always very helpful to have my babies on my lap to nurse and then fall asleep right where they were (I brought a small nursing pillow on the plane as my carry on and that was worth its weight in gold)...I flew with some as young as 1 month (funeral) and everywhere in between...and I always took an aisle seat...