Pitch .2/12

We recently added a 12'x24' deck to the back of our house. We also added a roof. The roof is 288 sq ft. The rafters are rough cut 2x6's, 22"apart. They rest on 3 2x10 at end and 2x8 at house. Yes attached to side of house not atop roof of house as we had originally asked it to be. (Don't get me started) this is why there is almost no pitch. The 3 posts at end of deck are 6x6's that are 8' in length. Not sure you needed to know all that and I probably forgot something. But we have the plywood up and need to know what roofing is best for our almost like pitch aka almost flat deck roof. Is metal roofing how we need to go as we get snow here in winter and already know we are going to have to roof rake the snow to avoid ice damns. We are not sure if we need to lay ice barrier down under the metal roofing either. So should we do a metal roof with very little pitch? Or would felt underlayment then the water barrier membrane and then another layer of felt underlayment suffice? We can't do shingles per the city inspector due to the pitch. Or is there a better option of roofing we are not thinking of! Also we are leary of doing metal roof because we don't like hearing the rain or hail hitting the roof. The sound is irritating, especially when trying to sleep at night. We have a metal roof on garage bad that is annoying enough when bin garage when raining. Please help us so we can get the best option.