I don't get to swim all that often these days, but when I get the chance I'm swimming, not sitting at the side of the pool,
I've got a couple of tankinis, but honestly, I don't much like them. I find them a bit problematic to swim in, because air gets trapped under the top, and in open water the wave motion often makes them float up. I prefer a good supportive one-piece, and for my money, the best value in those is Land's End.
The best LE tankini I've got is one that has adjustable drawstrings down the sides. Left fully open, they turn the top into something very close to a swimdress, but cinched up, they keep the top tight against your hips and help to keep the top from floating up. I've added a couple of rubber o-rings just under the outside leg of my suit bottom, and when I'm in open water I tie the drawstrings through those to completely prevent any float-up.
I do have one pair of swim-shorts that goes with my tankini, but I only use them for water parks; I prefer traditional briefs when I'm actually swimming.
RE: Land's End, note that very often if the suit has a halter top or straight shoulder straps, the plus-sized version will have cross-straps instead for better support.
PS: Remember that swimming is exercise, and it's good for you. Buy a suit that you are comfortable moving around in, because if it is only good as a "sit by the pool" suit you won't want to get into the water and play.
Looks are not really as important as comfort in this respect. Just buy something that covers enough to keep you decent, and don't worry about the prospect of a few bumps here and there.