III-IV+ rated rapids (May-June). Same as your company recommended, they told us running shoe type sneakers would work fine. That's what I wore with no problems. I wouldn't spend extra $$ on any special booties. With running shoes I cut my laces very short so that there wasn't much flopping around to possibly snag on debris on the river.

On a multi-day trip keep another pair of shoes in a dry bag for when your out of the boat camping.