You could try something like this:

With[
    {points =
        {{0, 0}, {1, 0}, {4, 0}, {1, 2}, {4, 2}}
    },
    Graphics[{
        Green, Rectangle[points[[2]], points[[5]]],
        PointSize@Large, Black,
        Point@points, Text[#, # + {0, 0.1}] & /@ points
    }]
 ]    

Using Tooltip instead of text:

With[
    {points =
        {{0, 0}, {1, 0}, {4, 0}, {1, 2}, {4, 2}}
    },
    Graphics[{
        Green, Rectangle[points[[2]], points[[5]]],
        PointSize@Large, Black,
        Point@points, Tooltip[Point@#, Text@#] & /@ points
    }]
 ]

This depends on what you mean by "better". What do you want to achieve?

A first comment: there's no reason to use Show in your code--just put everything in a Graphics:

Graphics[{Thick, Green, Rectangle[{1, 0}, {4, 2}], PointSize[Large], 
  Black, Point[{4, 2}], Text["(4,2)", {4, 2.1}]}]

As an alternative to having the text visible in the graphic using Text you can always use a Tooltip as in

Graphics[{Thick, Green, Rectangle[{1, 0}, {4, 2}], PointSize[Large], 
  Black, Tooltip[Point[{4, 2}], "(4,2)"]}]

then mousing over the point shows the desired text. But depending on what "better" means, I am sure there are many many possibiltles.