For the 14-year-old I'd recommend an iPod since it has a cachet among teens. Several models are available in your price range, even an iPod Touch can be had for around $200 if you find a used or refurbished 1st generation. For the 11-year-old it depends on their technical knowledge. An iPod is fine for them too but it's not as much a priority as for an older child so you could get him or her one of the many Sansa or iRiver products which are just as good as Apple products but are often cheaper. If they want video as well as music, the Touch is a good choice but some competitors have larger screens which makes it more pleasurable to watch a movie or video. One complaint about iPods is that you are generally limited to using iTunes to add content and it's very picky as to audio and video formats it will playback.
The last concern is how they plan to use it. The iPod Touch is small but not as small as the Nano or Shuffle, the Shuffle is so small it can be put into any pocket or just clipped to a shirt but you either need to playback the whole playlist or put it into random or shuffle mode. A hold switch is essential so that playback can continue while it's in the pocket, even if buttons get pushed accidentally, and you may want to set the maximum volume before letting them use it, to prevent overly loud playback that can damage their hearing. Some models let you use regular AA batteries which is handy if they forget to charge it regularly and can save your sanity on a rainy day. A final consideration is that the iPod Touch can also be used to play games, surf the net and even read books.

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