They are both correct; the difference is in the perspective of time from which they are viewed. "I was a student AT that school for three years" = you are, at the time of speaking, no longer a student there and are reflecting "I had been a student at that school for three years" = you are reflecting (telling a story in the past) which is set at the time in your fourth year at the school; i.e. three years HAD gone, when this happened. In context: "I was a student at that school for three years, but it's been demolished now." "I had been a student at that school for three years when they opened the new building there."