i'm not sure about white water, but many sit-on-top kayaks are pretty versatile and as long as you get the right width and length, should be able to handle offshore, inshore, river/creek, pond/lake. Typically for offshore you want something a little longer (to cut through the waves better) and something stable, 36" wide for example. But it can be a little harder to manuver that in a small creek or pond.
The reason is because sit on tops are designed to not sink (unless you bust a hole in your hull)