Nook does have a "shuffle" or "random playback order" mode.
It does have internal speakers so you do not have to use the headphones, which may or may not annoy everybody in your general vicinity.
A standard Nook has only 2gb of storage space, so you will have to invest in a memory card if you have a sizable music library.
I've got a relatively small music library (about 1.5 gb), so I didn't really need a memory card. But I got an 8gb card anyway, just in case.