How can I prevent my hero from auto-attacking?

When playing Nova I usually just keep her moving a bit back and forth. This works without problems, just make sure you click a bit further than where you'd want her to go, so there's no moment she's idle waiting for input. Just turn in time by issuing the next command.

S will just make your character stop and possibly auto attack as you've noticed already.

Hold down your right mouse button and just keep dragging it around to continually move. The great thing about this is no accidental attack clicks.