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
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
@dagery

Correct. All you need is a streamer digitally connected to the amp. As suggested a Bluesound Node is what many people start with and an end for some. If you want to get something that is comparable in quality with your current gear you might look at the Lumin or Bryston products.
As far as connectivity, generally, the streamer will need to be either Wifi Capable our connected via ethernet cable to your router/modem. Most people will tell you its better to have the streamer hard wired to the network especially if your wifi is shaky. I use a mesh network and have a mesh node sitting near my rig and then hard wire ethernet to the streamer. Purdy solid.

Deezer,Tidal and Qobuz are your services along with The Amazons for higher resolution.

Note. As I mentioned before you could get started with a nominal investment in a tablet that has digital out capability.