#1 son is about to turn 16.
He's asked for new headphones for his birthday.
Looking for some recommendations.

He uses them a lot when playing guitar connected to his amp.
Also listens to predominantly guitar / heavy rock music.
Suspect they need to be bluetooth compatible but also cable option.

thinking over ear rather than on or in ear.

Sennheiser. My bluetooth cordless rechargable ones have served me well for about ten years now

I've got Plantronics Backbeat Pro2. Nice enough, but I wouldn't recommend. They were good for the price at the time. The faux leather on the over ear sponges is thin and breaks down very quickly, it's the same on the headband. I'm on my third lot of ear sponges, and bought a zip on headband cover.

Friends have got the Apple over the ear cans, which are much better in my opinion, but they're about £500.

As Lee's said, Sennheiser are excellent (had them before). Also consider Bose Quietcomfort, or the Sony WH1000 XM6.

Gaz

Part-time audiophile here.

Firstly, I'd suggest that hunting for some headphones that can do the regular stuff, in addition to amp stuff, is a bit tricky. The music you listen to from Spotify, YouTube or whatever is processed and adapted for that use, whereas the signal coming out of an amplifier is 'raw'. Even if you stick a pair of Audeze into the back of an amp, without going through a DAC or other interface, it won't sound amazing. My advice with the guitar would be to pick up some cheap £40 open back headphones and call it a day. I think mine are old AKG ones - they wouldn't have been over £60.

Regarding the more simple use for headphones, there are a few options. I wouldn't bother with on-ear. They're the worst of both worlds. My favourite earphones are the Apple AirPods Pro 3. They just do a really, really good job. I've had other options - Sony WH-1000XM6, Bose QC Ultra, and I prefer the AirPods. Although, to be fair, that might just be because of the interface and ease of use with my phone. For running and cycling I use some Shokz OpenFit - mainly because they allow me to not be run over.

Headphones are a fair bit more complicated. My daily drivers, rather annoyingly, are the AirPods Max 2. The sound profile is pretty good and, for me, they're the most comfortable headphone I've ever worn. That being said, they are very expensive, the noise cancelling isn't great and the ear cups fill with moisture during use. I like them, but I'm not sure I'd recommend them, yet. I found the noise cancellation of the WH-1000XM5 to be much better, but I also found them horribly uncomfortable. I've tried the XM6 and they feel better, but by this point I'm used to the APM - particularly the fabric ear cups. My next favourite would be the Bose QC line (be it the Ultra or 35s) - either these or the Sony would be my pick for travelling. I haven't had great experiences with Sennheiser, and feel that there are better options out there. I like B&O, Bowers and Wilkins and, just like their speakers, the JBL Tour One. I also really enjoy my gaming headphones - some Steelseries Nova Pro. They're noise cancelling, 2.4, bluetooth or 3.5mm aux compatible, and are really comfortable.

Anyway, I could go on for hours. For your son, I'd probably suggest some AKG open-back headphones for the guitar, and then... well... whatever your son wants!

Find out if he wants headphones or earphones - I suspect earphones will get far more use and be far more convenient for him than a set of bulky, expensive headphones. Okay, yes, if used at high volume earphones can be a bit damaging (I limit mine to 80db, maximum), but so too can headphones! If I were 16 again (and it's not that long ago), I'd probably fancy some AirPods over headphones. The Pro 2 are good value in a deal, or the Pro 3 if not (there's not any difference between them that he will miss out on). FWIW, the regular AirPods are terrible - thoroughly do not recommend!

Happy to offer anything more specific.