I am restoring a medicine cabinet that has light bulbs on the top but no covering. Should I try to cover that area with glass (I'd like something frosted or opaque) or is there some type of plastic or other material that can be used?
A lot depends on the type of the lightbulb and the distance of the cover.
You could certainly use frosted glass, though acrylic is easier to work with and lighter weight. You can cut it with a saw, it's effectively "shatterproof," and the edges aren't sharp like glass.
Frosted acrylic sheets are available at many DIY "big box" stores, and online. You may know this acrylic material by the brand name Plexiglas.
Acrylic sheet is also available in a variety of patterns and textures, as shown on one manufacturer's website.
One easy way to go might be to find a replacement diffuser panel for an overhead fluorescent light fixture. and cut it to fit your application.