We just returned from HHI and let me tell you it was very very HOT! You can rent umbrellas, chairs, boogie boards and beach bikes from the life guards on the beach. The umbrella rental was $28 day to day. If you rented several days in a row the price dropped down to $17 per day. You can bring your own umbrellas and chairs as well and setup anywhere you want.
There are towels at the beach house, but I assume they don't want you to take them to the beach. We brought our own towels for the beach. We found we didn't use them because we set ourselves up at the beach house and just walked up there when we wanted to rest. The best part of the beach house is the air conditioned room. We have a 6 week old and with temperatures over 100 degrees with the heat index it was wonderful.
Have a great time.