Bluetooth or not

It will depend case by case. DAC used is the biggest factor. Newer Bluetooth technology can be quite good.   Traditionally, wired has greater upside.   Try both and see.

Using a good outboard dac with wired connection is probably the surest bet for best sound. I’ve gone that way with a Chord Mojo DAC. Not only is it great with headphones but as an input to a good hifi as well. I went for bust and connect it to line level inputs using a very high quality Mogami gold mini stereo to dual RCA Y adapter. The results are absolute top notch.

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.

Last year I purchased audio-technics ATH-SR6BT headphones.  They have Bluetooth and are wired.  The phones have controls on the cups for track switching and volume adjustment. The sound is balanced, with no frequency over powering another.