I don't think you'll need VPS. Just record files to .mp3, upload the files, and embed them in your site or allow users to download.
All of LunarPages' servers are in the US.
That's a good idea but it doesnt give the effect of a live radio show

Yes, I would suggest trying Basic out, then you could always upgrade down the road if needed. If you have any other questions, please feel free to let us know. Thanks!
When you say try basic out, do you mean just uploading mp3's or using it to stream a radio show (which would be against TOS on a basic account?).
If you are "broadcasting" other people's material, don't forget to get the proper clearances for public performance. You wouldn't want to go through all the trouble of getting set up, only to be closed down for copyright violations!
Aye that's nothing to worry about there, it will just be a radio show with speakers and guests.
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and another question what about using something like TeamSpeak? What would be the best and cheapest hosting to get for this?