Bluetooth or not

Wired is better. However, do not rely on the inbuilt DAC of most phones (Iphones are OK but most others not). As long as you are not hoping for the very best, but only for a big improvement with most phones, get a Behringer UCA 202 external usb DAC in between the phone and the amplifier for much much better sound (if you can get a usb signal out of your phone).
See here for more detail on Bluetooth quality: http://archimago.blogspot.nl/2017/12/measurements-oppo-sonica-dac-and.html

And I forgot the simplest solution: a Chromecast Audio, depending of course on what you actually want to play, and assuming you have wifi. Its analogue output plugs straight into your amplifier and is really rather good with 16/44. It also has an optical digital output for more ambitious use.

There are indeed two versions of what is called streaming: from the web (Spotify, Tidal, Youtube etc), and from your own server. Chromecast is primarily for the former, but with something like BubbleUPnP it will also do the latter.