These days, CD technology is commonplace enough that you'll actually see portable CD players in the $50-and-under category, which was the going range for low-end portable cassette players some 15 years ago. Don't expect too much from this price range--basic features and less-than-stellar sound quality--but you'll get at least basic CD-player functionality.
The average price for a decent portable disc player is about $100-200, for which you should expect good digital-to-analog converters (the chief arbiter of any player's sound quality), features like programmability and random-play, extended battery life (10 hours or more from two or four AA batteries), and some form of anti-skip protection to guard against interruptions in music playback due to jostling or bumping.
More expensive players will offer more features, better build quality, and sometimes, though not always, better sound. Features can include longer anti-skip buffers, longer battery life, equalization (such as bass boost), AM/FM radio, and spiffier headphones.
http://articles.directorym.com/CD_Players-a89.html