Don't replace one cheap, plastic watch with another cheap, plastic watch. There are plenty of reputable watch brands on the market that sell custom and high-end plastic pieces. Now that you've taken the grown-up step of buying a nice timepiece, plastic though it may be, you have to take care of it.
To remove scratches from a plastic watch face, dip a cotton swab in nail polish remover. Wipe the swab across the face and watch the scratches disappear. The remover is designed to melt plastic nail polish off fingernails and the same logic applies to the watch face.