Assuming the media you download are mp3-files any mp3-player would do, I think.
However, there's long thread here about players for audiobooks, which might be interesting, although it's not very recent: posts vary from 2005 to 2009: http://forums.cnet.com/7723-7595_102-56870.html
Of course, all an mp3-player does is playing mp3's (and sometimes movies, but that's not really mp3). If you want to run the program, that probably requires Windows or Linux or MacOS, so you would need a laptop or netbook or possibly a tablet. The deciding factor here: the minimum system requirements.
Kees
I am looking for a device to download media from Rosetta Stone so that I can utilize the program while traveling/flying. Can anyone give me some sound advice on what would work best?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic