The licence would have to be purchased for the country the owner lives in, making sure it has permissions to play music in the country the station broadcasts to. For instance, if the owner of a station lived in the UK, but broadcast in the USA, they would need licences from PPL and PRS.
Regulatory bodies represent copyright holders across the world so a licence from your native organisation should cover you for any music you will be playing.
At the bottom of this article is a list containing the names of regulatory bodies across the world, as well as links to their websites. However, this list is not comprehensive, so if your country is missing it is best to contact your local government for information on which organisations provide licences.
Yes, you will be required to pay a one-time licence fee that grants you a licence to play the music wherever you want, as many times as you want without further cost. Royalty free sites include:
Jamendo Music: An independent music community.
Audio Jungle: Thousands of tracks available for just $1.
Storyblocks: Offers music, sound effects and jingles.
And if you would prefer to have something more unique there are websites such as Fiverr, an online platform where session musicians offer their services for a fee and can compose and record music for you which can then be used again and again.