What do you mean for your own graphical operating system ? something like windows ?
I suppose you want to do it for your own personal satisfaction, ok, i'd follow this route
first : low level access to graphic device , write and read in a 'graphic buffer' in different resolutions.
second : create fast graphic routines : pixel plotting, line, rectangles , ellipses ( for drawing circle under different x/y screen ratio )
third: font rendering ( in my experience this is a real pain in the a** ) , because you have to compute text metrics, word wrapping,
text scrolling, and scissoring.
forth: window handling , basically rectangles where you can draw in , borders, layouts ( i had already done and its another pain in the a** )
fifth: input handling, mouse, keyboard ( low level interrupt )
sixth: low level disk access ( semaphores , multiple files opened )
you may want to start in a different order, but this is the minimal build for a OS , 1.5 years ago i started writing an opengl gui and i had
to work out many of those different problems, so talking about the graphic side,it was a very intensive task.
Good luck, if you need some graphic algorithms, like word wrapping and such , let me know.