I have tried a lot of different footware while water hunting over the years. I already stated above my preference, by for those still considering, let me explain why.
1, barefoot, no. just don't even think about that. The beaches are full of broken glass, torn up aluminum cans, broken shells, broken coral and lots more that will tear up your feet. This is a trip to doctor just waiting to happen.
2, sandals. better than barefoot, but far from ideal. Cheap flip flops will break from repeatedly stomping a scoop into the sand, plus they like to float off and are a general PIA. Cloth "TEVA" sandals are better, but the cloth straps are really bad about collecting fragments of coral, shell and sand which then grind on your feet and ankles like sandpaper. All sandals still leave you open to cuts on toes and feet.
3, tennis shoes, better than sandals but the fact they are open at the ankle means sand, shells, coral, etc will continually get inside forcing you to periodically stop and empty them out. Shoes weren't meant for surf and they will break down a lot faster than on land.
4, dive boots. They have hard soles so you don't have to fear stepping on things in the water (stingrays not included). They are close-fitting around the top to keep out the vast majority of sand, etc. Yes, you will still get some in but I have never had enough to be a bother. The height plus zipper means they are staying put and you don't have to fear them accidentally coming off. they were made for a marine environment and will last a long time in the surf.
the down sides of scuba boots, yes, you will get sand in the zipper and may have to work it a few times to get open, but I have never had a pair I couldn't open and I have never broken a zipper either. Just stick a garden hose in the zipper base and inside the boot to wash out sand after each hunt. Neoprene WILL stink (especially boots) if left wet. I recommend leaving them to drain in a well ventilated spot, out of direct sunlight. If you forget and leave them in the trunk of your car, you probably wont do it twice. An occasional soak in an enzyme like "sink-the-stink" helps too. A good pair of scuba boots aren't cheap, but you do get what you pay for. Buy a no-name, cheap neoprene boot and you might as well buy a dozen. Buy quality once, or cheap over and over again.