Lucky you to win a trip!!!! Congratulations. Anyway.....everyone who has paid for a ticket on the plane will be able to bring a carryon bag, that fits in the airline configurations, check their website for measurments, and a handbag, briefcase..that sort of thing. We always have a backpack/totebag and I have my 'large' handbag also. In that carryon are the following things....tickets, itinerary, park passes, book, meds, quart sized ziploc bag with 3 oz size of toothpaste, mouthwash, hand lotion, sunscreen. If your kids will need anything to occupy them, it should go into their own backpack. The backpack will fit underneath the seat in front of them. Do not overpack your carryon though. You will find you don't need as much as you think you will.
Check out the TSA site to find what you are allowed to bring with you.
Have a terrific trip. I arrive the same day you do....here's hoping for some nice weather!!