Wear gloves.Those nitrile exam gloves you can get at the supermarket or Costco will be enough to protect your fingers. Your arms will be exposed, but usually sensitivity starts with stings to the fingers, which encounter most problems. I've known one aquarium store owner who developed serious skin issues after many years of hands-in-tank multiple times a day---and there are many things that sting, to which you can develop so much sensitivity you can't tolerate the water itself. Also, it costs an animal to sting you, meaning they lose spines or the like and have to repair the damage, so it's better for the animals if you wear gloves, which will not trigger a sting or damage your corals.
There ARE some venomous creatures we commonly keep, like rabbitfish, lionfish, and so on. Be aware. I had a rabbit once, and when working where I was apt to provoke it, I wore not only rubber gloves, but leather gloves underneath the rubber: I've seen a rabbit-sting mark, and it looked fair to cost a guy his thumb. Black and not-good. Sea mat is another. We have a sticky up top of the forum on the hazards: read it before you buy. Wear glasses or goggles when 'fragging' a coral, meaning taking a sample off to grow a new coral. Live coral in the eyes is not a good thing. Again, reasonable precaution.
The good news is, I've kept tanks from long before they ever issued warnings, I do wear gloves, I do recognize that getting 'finned' by any fish is not good, and I have had no problems in decades of doing this. So reasonable caution is enough unless you want to go in for the few species that really can do you harm.