The Amazon Robotics Challenge enlisted sixteen teams to each design a pick-and-place robot for autonomous warehousing, addressing development in robotic vision and manipulation. This paper presents the design of our custom-built, cost-effective, Cartesian robot system Cartman, which won first place in the competition finals by stowing 14 (out of 16) and picking all 9 items in 27 minutes, scoring a total of 272 points. We highlight our experience-centred design methodology and key aspects of our system that contributed to our competitiveness. We believe these aspects are crucial to building robust and effective robotic systems.