AIFF and Apple Lossless Encoder files won't play on iPod shuffle (1st and 2nd generation). However, you can convert these file formats to AAC for iPod shuffle play.
To identify the different iPod models, see this article.
To do this, just select the "Convert higher bitrate songs to 128 kbps AAC for this iPod" from the Settings tab when iPod shuffle (1st or 2nd generation) is selected in iTunes. When this option is selected, songs are converted to 128 kbps AAC files when you transfer them to iPod shuffle (the song files in iTunes aren't affected).