I see all kind of mp3/fm players on ebay (no name brads). Are mp3
players prone to easily break down? Just wondering if I should spend the
extra buck and buy a name brand that will not easily break down.

Most flash-based (no hard drive, 1GB or less) MP3 players are pretty
reiliable. It takes a lot to kill one. Static is your biggest enemy,
and it's really rare to kill a player with static. No-name brand should
be fine.

But if it's a hard-drive based player, go with a name brand. Not that
the parts are any flimsier, but the software is usually bad, and that
affects the sound quality, battery life and usability.