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. These often come with most 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 legrope. 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.
Covers for bodyboards range from basic towelling 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. Bodyboarding is not a team sport so above all choose the equipment that you will be happy with.