What REST PUT/POST/DELETE calls should return by a convention?
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).
Forgive the flippancy, but if you are doing REST over HTTP then RFC7231 describes exactly what behaviour is expected from GET, PUT, POST and DELETE.
Update (Jul 3 '14):
The HTTP spec intentionally does not define what is returned from POST or DELETE. The spec only defines what needs to be defined. The rest is left up to the implementer to choose.