There are a lot of dish detergents out there that will work well but my personal favorite is Dawn. I use the original scent version which is turquoise in color.
So what is Dawn dish detergent good for? In one word... plastics! Dawn is very good at cleaning plastic parts or degreasing metal parts. It also is really good at removing grease from your hands.
I use an old soft toothbrush to clean plastic parts. I run it under water and apply a small amount of Dawn dish detergent to the toothbrush. I also premoisten then parts to be cleaned. Then I use the toothbrush to gently (or not so gently for playfield posts) clean the part. Keep the brush and the part wet for better cleaning. I sometimes soak parts in a solution of Dawn in water if they are really dirty. (Do not soak parts with graphics on them!)
I do not suggest that you use Dawn on plastics with graphics on them, but I do. I moisten the plastic with water, put a little Dawn on the plastic, one side at a time, and gently scrub the plastic with my thumb and forefinger. I only do this with graphic plastics that are in very good condition and are very dirty. Always be sure to gently, but thoroughly rinse all cleaned parts with cool water.
Dawn leaves a lusture on any plastic surface that playfield lights reflect off of very nicely.