Plot a precise Cartesian graph of x^2 + (y - 1)^2 = 4. The graph must show a perfect circle centered at (0,1) with radius 2. Include x-axis and y-axis with equal scaling, grid lines, and numeric labels. Mark and label points (0,1), (0,0), (0,2), and (0,-1). Ensure it looks like a real mathematical plot, not artistic or stylized.