Check with your local dive shops for when they are going to offer their next Introduction to Scuba. For little or no cost they will take you to a local pool, get you used to the equipment and get you in the water and let you blow off a tank of air to give you a taste of what it's like.
My son and I are advanced divers. He just took his fiance throught the Intro to Scuba with our shop. She loved it and now wants to complete her certification.
Breathing underwater - no problem. Strange feeling at first - breathing where you know you shouldn't be able to, but you get used to it immediately.
Sharks - no worry. The only times I've seen sharks are when I purposely took shark dives. No problems - survived without a scratch. It was truly amazing to be in the water with these beautiful, amazing creatures. I've done it twice and I would do it again.
To experience weightlessness is awesome! Reef, drift, shipwreck, wall diving, cave diving, cenotes...there are many different ways to enjoy the underwater world. Go for it!