SCUBA
I highly recommend SCUBA diving. It is very beautiful!!!!!!!!!!! My husband and I use to snorkel while on vacation, then about 5 years ago we decided we would both get certified before the next vacation we took. My husband, jumped right in and was comfortable right away. I on the other hand had to try it a couple times before I decided I really liked it. And I was fairly comfortable in the water ... but had to adjust to all the equipment. NOW I LOVE DIVING!!
Our last diving experience was in Jamacia and we didn't need to wear wet suits. So I don't think you'd need it in the DR either. Yes, you can rent all the equipment from dives shops and at the hotels. And most of the hotels have the "quick" PADI certification. All you have to be able to do is swim ... and basically you don't even have to know how to swim correctly. Then they'll take you down on a shallow dive, something like 30-35 feet.
My own opinion is I'd rather be certified and know how all the equipment works than do the quick course at the hotel. There are also tricks you learn in the real classes, like how to get the water out of your mask while under water, what to do if a part of your equipment gets caught on something etc. And it's not that expensive to become certified. I think we paid about $200 U.S. But we have friends who have done the hotel thing a few times and are fine with that.
Oh, and your other question was if it is "physical." No it's not at all physical. If fact the slower you move and the calmer you remain the better your dive experience will be.