Go for a TPU or silicone based case with a textured grip on the sides and a raised edge around the screen and camera. That combo handles clumsy drops better than hard plastic and it stays steady in a sweaty hand during a jog. If you can find a dual layer design with reinforced corners in your price range and even better. Works great.
Waterproof at twenty bucks is rare. Aim for splash friendly features instead such as sealed buttons and a snug flap over the charging port. If a stand matters, look for a low profile kickstand that locks firmly so it does not rattle, and check photos to be sure it still sits flat in a pocket. Double check the cutouts match your ports and the buttons click cleanly, and watch the thickness so it does not turn your phone into a brick.