Streaming virgin


I know this is a broad topic but I have to start somewhere. Up to now my source has only been my cd collection. I would like to get into streaming to discover new music.  My current system is modest consisting of a Simaudio 340ix integrated and 260d transport.  Speakers are Focal936.  I currently have a Spotify premium account that I use with my Amazon kindle tablet and ear phones.  I do not have a PC at present. So, where do I start?  Will I need additional equipment ie computer, server, etc?  I am pretty ignorant with all this tech stuff.  I'm looking to get quality sound as easily as possible and if I have to spend a few bucks to do so thats ok. 
dagery
That integrated has an 1/8 inch mini jack input on the front of it. Have you tried using that with the kindle? you mentioned you were using earphones. Of course this will be using the crappy DAC in the kindle.
Is there a DAC within the integrated amp or transport?

You may already have a DAC and only need to have a streamer to your system.  
@mrklas
Yes that Amp should have a ESS9018K2M according to the user manual.  That is why I was recommending going digital in.

Then as a subsequent step you could fire up a trial subscription of  Tidal or Qobuz and try hi rez to see if its worth the spend. Deezer is also an option and streams at RedBook CD quality and has a vast music collection.
OH!  @dagery if the Moon 260 is a "D" it should have a DAC as well.  Does the CD player have digital inputs on the back?  Or was the unit $2,000 or $3,000?
@ jbuhl 
The ads say that the DAC is an option. So the OP may not have that option installed. That may be a route to get his feet wet as well, depending on cost. And it may be a plug in option