J.F.
Definitely take the snap and go with the car seat. You are going to need to take your car seat with you for when you get to your destination and travel by car. Also, a 3 month old can't see too well anyway and she won't miss anything she can't see. :)
Pack what you will need for baby in a larger diaper bag that you will carry on. Pack enough for 3 days...you never know what will happen to your flight (delay) or baggage. Pack an extra outfit for you in case baby spits up.
They have special lines at security for families. Don't feel rushed about it, just follow their directions. Try to remember that you will have to hold baby through the metal detector without any blankets. Everything else will have to go on the conveyor belt. They will hand check the stroller and car seat. Remember to keep all liquids in 3 oz or smaller containers and put them in a quart ziploc bag. Have that bag ready when you enter the security line as well as your ID's and boarding pass. You won't be able to take any drinks for you or baby through the line. They MAY let you take a bottle, but don't count on it.
Gate check both stroller and car seat. It won't cost any extra and will be less damaged than if you checked them at the ticket counter. They are the last items to be loaded and the first to be unloaded. They will be sitting there for you when you exit the plane and will be a God send when you need to walk through the new airport. I have had little to no damage to our stroller or car seat by gate checking it.
Check the pack n play with your other baggage. That should also be free, but double check the airline's policy about how many items you can check for free for baby.
Make sure baby has something to suck on when you take off and land. And you might want to take a sling to hold baby while you are on the plane.
Good luck and have fun!