Dextromethorphan and a productive cough

I'm sure this is pretty trivial, but I honestly don't know the answer. Or if it even matters.

Problem: Person presents with chest congestion and a productive cough. You prescribe clarithromycin 500mg bid for an upper respiratory infection, and now they'd like something for their chest symptoms.

I would typically recommend an expectorant — either plain Robitussin or Mucinex, depending on their financial situation — and instruct them to drink plenty of fluids. Is it better to keep them away from DXM-containing products? Will they get better more quickly if you don't suppress the cough? It's my experience that guaifenesin quiets a productive cough somewhat anyway, but not as much as with DXM. Are they better off doing some coughing? Assuming, of course, that they aren't hacking their lungs out.

Does it matter one way or the other?