Translation:Whose jacket is this?
From my experience, all three are relatively commonly used, with the most common being コート I think.
I'm not a native speaker, but I think each refers to a subtly different group or sub-group of clothing. I think 上着 is a catch-all term for any type of jacket, but also generally meant a blazer or formal jacket, while コート was for thick coats designed to stop the cold/wind, and ジャケット was for thin sports jackets and the like.
(I lived in Sapporo, so maybe that's why コート seemed like the most common one for me f(^_^;)