The first pieces of personal gear that you should bring to the dive are a mask and snorkel. The mask will be used throughout the entire dive. Taking your own mask is extremely important because it makes sure that you have a pleasant dive. A really tight mask that squeezes your nose too much or a loose mask that leaks in water can ruin your dive easily. Many people use goggles while snorkeling or doing shallow dives because of the comfort, but those tend to place way too much pressure on your face as you go lower and lower into the water. The snorkel is used when you are first getting into the water and deciding where you are going to dive to. Plus there are some dive areas that are extremely shallow where using your scuba equipment would be a waste of oxygen.
The next piece of personal equipment that you should bring with you is a pair of flippers. Many first time divers think that their legs will be strong enough to propel them through the water, but once they are about 30 feet underneath the heavy water they usually realize how well the flippers would work. You need to bring your own because flippers are just like shoes in how they fit your feet. Some may be too skinny or too long even if your shoe size appears to match.
Another piece of equipment that is needed is a watch. Even though the diving instructors or captains may provide gauges that show how much oxygen is left, you may feel safer while diving having a watch that shows how much time you have been under and the estimated time that you should come back to the surface.