My daughter took her first flight at 3-month old when we were moving back from Europe, since then she has been on 7/8 round trip flights mostly to west coast (she is turning 2 this week). I used to carry her in Babybjorn baby carrier in front of me until she got too heavy, so I had both hands free for diaper bags, carry on etc. And I can use the toilet with her in front as I travel without my husband most of the time. Then I started purchasing her own seat at 9-month old (some airlines offer discount infant fare) so she can travel more comfortably for the 4/5 hours flight. Or check with airline on how full the flight is going to be, if not too full you can probably take up an empty seat next to you to give you more room. I used to nurse her during take off and landing to ease ear popping then make sure she munched on cherrios or goldfish when she was able to chew.
I usually pack back-up liquid formula, bottle, sippy cup, homemade baby food, snack (cherrios, gold fish, wheat crackers, fruits etc. but sugary candies/cookies/snack), cold and fever medicines just in case. Just make sure you let the security know and show them. DVD player is a plus but not necessary. Instead, I pack stuff animals she can't sleep without, blanket, favorite books, non-noise making toys and at least one extra outfit for her and a few more diapers than you think you need.
Car seat is up to you , I usually do when there is car ride involve at the destination since ours recline so she naps better without bobbing her head. Stroller is a must for trips. You can check in at the counter if you don't want to stroll through the airport but it really helps with diaper bags, carry on etc. until the cage. As you are traveling with your hubby, one of you can push the stroller without problem (unlike me, I usually carry a backpack diaper bag, a rolling carry on with extras and back-ups in case luggages don't made it and push the stroller myself).
Good luck and have fun on your first family flight.