There is a whole subculture of people in the world who prefer their plastic digital watches over expensive analogs. But don't think that your plastic, quasi-geeky watch won't have to be maintained and repaired. Plastic can scratch, too and sometimes those surface imperfections can be harder to fix than glass.
Is your plastic watchband a bit grimy? Put a dab of toothpaste on the band and gently rub it with your moistened fingers. Rinse clean, then dry with a soft cloth. If the watch itself is not water-resistant, be careful not to get it wet during the process.