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
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
The cd is the transport. The amp has the dac.  I was hoping to maintain at least cd quality.  I would subscribe to a better streaming service for that purpose. So am I right that all I should need to do is add a stand alone streamer to my current system?  If so is that then just a wifi connection thru an app?  I forgot I also have Amazon HD music service