We just had our first flight with our 1 year old. It went pretty smoothly.
If you decide to buy a ticket for him to have his own seat, you need to make sure your car seat is approved for flying... I'm not sure how that works, so you might want to check on that. Check out www.faa.gov/passengers/childsafetyseats for more info.
He can sit in your lap for free until he's 2 years old. You'll need to bring his birth certificate for proof of age.
Next time I think we will get her a seat of her own. She was pretty restless and climbing all over us. She eventually fell asleep, but we were exhausted!
You can check your stroller at the gate. I definitely recommend that! That way it's there for you until you board the plane and as soon as you get off. You don't have to worry about carrying him all over the airport.
You can also check your carseat & a pack n play if you need to. If your renting a car at your destination, most rental companies can provide a carseat. You can also rent a pack n play or crib at your hotel. We did both and it saved us a ton of work and worry.
Make sure to carry on a few fun toys that are either new or that he hasn't seen in a while so they hold his interest.
You can't bring in your own drinks (except breastmilk & formula), you have to let them know you have it though. I brought an empty sippy cup and just filled it with bottled water after we cleared the security check.
Definitely check with your airline (they should have something online) about traveling with children. Southwest has some good travel tips on their website.
Also... you can save packing space by buying diapers at your destination.
Whew... I've written a book! I know how stressed I was flying with my daughter the first time, so I really hope some of this is helpful!
Good luck!