There are two general types of water shoes on the market - water shoes and water sandals. The latter usually have wide vents or small holes to release water and help your feet dry quickly, but both types usually have closed toes to protect your feet from rocks and underwater objects.
No matter what style you choose, there are a few key features to look for. A good water shoe should be comfortable and lightweight so you don't get dragged underwater when you swim, but it has a hard rubber outer sole with indentations (also called "lugs") that provide good grip so you can confidently walk on wet surfaces, such as coastal rocks or riverbanks. Look for a hard rubber toe cap for added protection, and a lightweight primary material such as mesh or neoprene that will dry quickly when you get back on land.
Check the fit of your new water shoes - bungee or lace-ups are ideal for making sure you're comfortable on your feet while exploring. Make sure there is no tightness or chafing anywhere, especially around the toes and heels. If you're looking to buy a new pair of water shoes, it's a good idea to choose a pair that you can walk in as well as wear, and that looks stylish enough to wear casually so that you can wear them comfortably.
As mentioned earlier, the best water shoes are usually not waterproof. If walking is your first choice, and you only need to deal with puddles and showers.