"What is considered an acceptable angle for a roof to ensure that there will be sufficient run-off during rain conditions?"
Generally, minimum slope for water to run off is 1% (1/8" per 1').
However, minimum slope for a flat roof by building code here is 2%. (1/4" per 1').
You have more than enough slope for your roof, however you will likely need some sort of membrane roofing since it is very low slope.
There are profiled metal roof cladding systems specifically designed for low-slope application. I don't know if any would be good for a slope as low as what you've got, so that is something you would have to look in to. Maybe call local roofing supplier and see if they have anything that would work for you.
The lowest slope you can do for a shingled roof (that I know of) is 1 in 4.