In the US, there are statutory licenses that enable people who are doing broadcasting or streaming, to pay a flat fee for all the music they play. This is so they can avoid individual agreements with the thousands of musical artists they might want to air or stream. The Library of Congress set the minimum rate, under law, that you have to pay in the US for a webcasting statutory license, which you can find here: http://www.copyright.gov/carp/webcasting_rates_final.html . Again, this is if you choose to use a statutory license and don’t otherwise negotiate a different agreement. If (just for example’s sake) Island Records agrees to let you play all of their artists under a different license, for a different price, you could operate under that, instead.
Some people decide that they are going to work with a company like Live365 to both host and manage their streaming; someone I knew who used them, had to provide ASCAP/BMI reports to them on the incidental music they used. Others use a company like http://www.streamlicensing.com/ which ties in with SoundExchange, which manages most of the streaming stations’ statutory music licenses.
Bear in mind that there is copyrighted music you can use freely, which is listed under the Creative Commons license scheme. It’s still copyrighted, but the license may allow you to play material if you’re non-commercial, or simply if you just provide attribution. There are many artists who have made Creative Commons-licensed music available on Soundcloud and on Jamendo.com.
And, if you’re only negotiating with a few artists directly, you can make arrangements that don’t require the statutory license.
I suspect that something like Stream Licensing would be a good bet for you, whereas I personally negotiate with individual artists and use Creative Commons-licensed work.