Welcome aboard, Amanda! You must be considering - or maybe you are already - booking a magical cruise with Disney Cruise Line! I promise you're in for the trip of a lifetime, Amanda!
GTY is short for Guarantee. Some guests book a stateroom without knowing the exact room number, which is called a "Guarantee", because Disney guarantees that it will be in the
category the guest pays for or better. This is a nice way to book a room if a guest is not too particular about the location of the stateroom. For instance, you might book a category 9A Guarantee. This means that you will pay that particular price for a 9A stateroom and a few weeks before you set sail, will find out what stateroom you will have. You will have at least the Deluxe Oceanview Stateroom you paid for, however if that category is sold out, you might luck out and be assigned a higher category, perhaps including a verandah. It's a gamble, but again, if you don't have a particular part of the ship in mind, and don't mind waiting to find out your stateroom assignment, there is always a nice chance that you could end up with a better stateroom than you paid for.
That being said, you can't go wrong with any of the categories. My family is happy to sail inside, with a porthole, or with a verandah on any side and any part of the ship. As long as we're sailing with Disney Cruise Line, we know we'll have excellent service and lots of family fun, no matter where we rest our heads at night.
I hope that helps as you continue to plan, Amanda!