I usually have a bikini. I like that I can get different sizes on top and bottom, since I'm a pear, and that the tops are often sized in bra sizing which is easier to fit. I've not done any serious swimming for exercise for a long time though - in that case, I'd probably get an athletic suit (speedo or something) but honestly even then I'd consider the two-piece ones for fit reasons
FWIW, I have had 2 wardrobe malfunctions where my bathing suit slipped down while swimming. Both times, it was a one-piece.
Tankinis don't work for me at all, even though the concept is great. The top part is never cut right to stay down over my hips so they roll up and expose *just* the muffin top. Not a good look.