Overall, the conventions are “think like you're just delivering web pages”.
For a PUT, I'd return the same view that you'd get if you did a GET immediately after; that would result in a 200 (well, assuming the rendering succeeds of course). For a POST, I'd do a redirect to the resource created (assuming you're doing a creation operation; if not, just return the results); the code for a successful create is a 201, which is really the only HTTP code for a redirect that isn't in the 300 range.
I've never been happy about what a DELETE should return (my code currently produces an HTTP 204 and an empty body in this case).