Remove the fluid from the MC first. You can get all the nasty fluid out of the MC first, instead of pushing it through the lines. After you clean the mc, fill it with new fluid and then bleed the lines.
My personal way is to open all four bleeder valves and let it gravity bleed for an hour or so, before starting the bleeding process. Put a board under the brake pedal to make sure it doesn't go to the floor while you are bleeding.
Do the work on flat ground, and when you are done, pump the brake pedal before you try to move the truck.