We just returned from a week at Hilton Head and our kids' first trip to the beach (2 and almost 4).
They were so much more excited about being in the pool at the house instead of the beach to our chagrin. Regardless, we made them go to the beach at least a few hours each day. They didn't love the water, but they loved digging in the sand with Daddy.
So, my recommendation is a good shovel. Not the ones that come with the play sets. If you're driving, take a good shovel. Take a wagon to get around if it's not all centrally located where you're staying.
Our son loved playing with a water gun the whole time. We also took a large frisbee ($10) that he had fun with on the beach when the winds weren't too high. Water shoes weren't necessary. Neither of our kids really cared about having them on. We'd gotten some at Target for $8, and they did fine. A Boogie Board would probably be good for your kids at their ages as well as something to put shells into. A large sand bar kept almost all the shells from washing onto the beaches in Hilton Head. Bummer for the kids.
Our friends brought beach chairs and a few umbrellas which were REALLY nice. Otherwise, the kids went out, did their thing and had a great time. Just being there and letting them experience a different environment will be a huge step towards having a blast.
Have a great vacation.