Shoe polish is alright to use, but you shouldn't use it on non-leather or it'll just wear off. Dye works better to recolor discolorations.
Scuffs and scratches on shoes are rough, man. The best way to take care of them is to clean the area using a good cleaner (i.e. there are a bunch out there, but Mr. Clean Magic Erasers, the spot pens, and Jason Markk are a few good ones). Then, if the color doesn't match you should use a dye that is the same color as the rest of the shoe. When it's all done, you should use some sort of protectant to make sure it doesn't happen again.
The best protectant that I've found is SKUFF Protective Coatings. Other ones like waterproofing sprays, protectant sprays, and waxes generally just wear off and don't do much at all in the first place. SKUFF adds a finish that prevents scuffs/scratches in the first place, so your shoes stay looking new. It doesn't hurt that it also repels stains, water, and dirt to keep your shoes clean. Best part: you apply it once and it lasts for years.
Best advice I can give IMO. Good luck!