Removing the old "asbestos" roof might be the biggest part of the cost. My understanding is that they are not a hazard unless/until you do anything with them. I don't think you can DIY it, the tip (aka recycling centre) won't take it.
So the total cost might not change much if you choose better materials. I see the shed is concrete block so should last a few decades more. Wouldn't be worth spending ££££ on a wooden one.
Noise? I stayed with friends in a nice interior pine clad chalet in the Mamores (Kinlochleven-ish) twixt Christmas and new year a long time ago, had a corrugated metal roof with lots of insulation. We had a week of gales, hail and heavy rain, even shouted conversations were difficult, as was sleep. Got lots of walking in though, much quieter outside than in and what else do you do if you wake up long before dawn. Well yes, that, but it doesn't fill the day.