I was personally thinking of putting the songs in as notes, that way you can listen to them in your pipboy at any time. Figuring out where to put a couple dozen songs would be difficult, though, and would probably lead to a ton of conflicts, so randomized loot is probably a better idea. It should still be easy to add them in as notes, though.
For turning them in, my plan was to put in a terminal in the GNR building that uplinks to a song database, or something like that. There'd be one in the Lucky 38 for Radio New Vegas, too.
Now to figure out how the radios work... If anybody can help with this, I'd appreciate it very much. I know insofar as they're quests with a ton of dialogue attached.
ed: As to Three Dog living in a broadcast station, it's my personal assumption that the EMP from the nukes wiped a lot of holotapes, or...something. Probably going to use that as a justification in the database uplink.
I feel like I should mention that there's also a lot of really cool shit under Creative Commons, as long as where you know where to look. Public domain vintage songs are a far safer bet, but hey, if you can find neat modern jazz that doesn't clash that could be cool too.