As many women are rightly concerned about the feeling of thongs (a.k.a. the wedgie), when shopping, look for the thinnest fabric available.
The butt of the suit will shift slightly, but if the entire swimsuit becomes a wedgie it is not a good fit for you, and you will spend the entire day pulling and tugging at it.
High-pressure activity, like going down a water slide, is the source of many a painful and exposing wedgie, for both men and women.
They shouldn't give you a wedgie, they shouldn't bind or chafe, and you should feel sexy in them like you would feel in any other pair of denim pants for daytime.
If you have a long torso, you can purchase your top and bottom separately, allowing you to find a suit that covers you up and doesn't give you a wedgie.