Consistent Pressure Gives a Uniform Look. Keeping a consistent pressure with the crayon on the paper gives a uniform, pleasing look. If you're pressing hard, your hands will get tired quickly, so I prefer to press lightly. Interestingly, being aware of how much pressure you're applying seems to be really hard for younger children. It must be tied to motor skills in some way. It won't hurt anything to tell them this tip, but if they aren't implementing it, just let it go.
For beginners I would suggest either the Staedtler or Faber Castell brand of pencils. These produce significantly better results than bargain bin pencils, provide good colors and allow you to try some simple shading and blending techniques. With practice the best coloring results can even be achieved with the most modest tools!