Hi,
If your Amiga has USB, most of the non-DRM-crippled MP3 players will work fine as they use the standard mass storage device driver to operate when transferring files.
However, DRM-crippled players (iPod, Zune, etc) that aren't switchable to use the mass storage class (some are) will be unlikely to work with the Amiga unless someone writes specific driver software for it.
As for the AMV file format - forget it. Video converted into this format looks crap even on small screens and takes up tonnes of space - not the ideal combination for small devices. It's basically a cop-out format that requires little CPU power to play back and is used on cheaper so-called "MP4" players that don't have enough grunt to play back real formats.
And I'm not quite sure why you think Amiga is "back in the business"! It appears to be mainly in the business of doing nothing much at all...
- Ali