Headphone Recommenations

I would not buy headphones with Bluetooth, and if I did I wouldn't spend that much. Bluetooth headphones are more for convenience than audio quality. The Sony Sony WH-1000XM3 seem to be well regarded.

Perhaps you can elaborate on why Bluetooth is a must have? Most members here are focused on sound quality and two channel stereo systems with speakers and not as much on headphones. You might have better luck on headfi or Reddit.

A great pair of headphones in your price range are the massdrop Focal Elex. No Bluetooth though. 

Another option you might consider is a closed back headphone to not bother the rest of your family.  It won't keep all of the sound in the headphones, but will be much less of a distraction to others.  I have a pair of Audeze LCD-XC (no bluetooth) that I really like, but those are a little out of your price range.  I also really like the Massdrop x Fostex T-X0.  I think those were about $150 (no bluetooth).  The T-X0 sounded really bad at first, but after 50 or so hours of break in it opened up.  It's still a "dark" headphone, with more emphasis on bass than treble, but it's still revealing and very easy to listen to and comfortable to wear.  It appears to currently be sold out on Massdrop (now called Drop.com), but you might be able to find some used ones.

Keep in mind that for most headphones you can get longer cables or extension cables. 

For your stated use Bluetooth might be OK.  I listen to Tidal, Qobuz, Spotify, Radio Paradise, etc. in my car via Bluetooth and the sound quality is pretty decent, but a car is a much different listening environment than sitting in your living room with headphones on.