Once you have chosen a bodyboard the only other things you may need (apart from a wetsuit) are a pair of flippers, a wrist leash or leg rope and perhaps a cover.
Flippers or swim fins
When trying on flippers make sure they have an 'open heel' to let the water pass through the strap ('closed heel' flippers tend to get pulled off more easily in the surf). The blade area of a surfing flipper should be short and stiff to enable rapid kicking in short bursts for catching waves. You may find some brands of flipper more comfortable than others, as flippers last a long time it may be wise to spend a little extra if it means getting a good fit. (Lycra or thin neoprene flipper socks can greatly improve comfort).
Wrist Leashes
These often come with cheaper boards but are not supplied on more expensive boards as some riders prefer to have a leash on the left or right, or a leg rope. Some riders don't use a leash at all. The most common type of leash is the coiled wrist leash. Neoprene padding on the wrist strap is a good idea for comfort.
Bodyboard bag or Cover
Covers for body boards range from basic toweling to heavy duty padded nylon. A cover with a large outer pocket and backpack straps is a good idea if you're riding a bike or walking a long way to get surf. Buy the cover that best suits your needs and budget.
Before you part with your hard earned dollars take the time to think over the various choices available to you. Body boarding is not a team sport so above all choose the equipment that you will be happy with. Often your choice can be swayed by peer group pressure or advertising hype. Some pushy salespeople will even bad mouth brands they haven't got to try and make you buy one they have.