https://www.anker.com/ca/products/q20i-a3004z11 This one is BT but has a wired option, I think the ANC works in wired as well. They're very highly reviewed in the budget ANC category for both noise cancelling and sound quality. I bought a set for my wife and kids (I already had a set of Audio-Technicas, so I passed for myself) and they all like them quite a lot.
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Sony XM and Bose QC are kinda the gold standards here. You can get an older gen of the XM for cheaper without missing out on much
I find I don't use my XMs enough on trips to want to carry around bigish headphones, so I picked up the technics eahaz100 recently and I've been super happy with them. Something else to consider if you're open to earbuds still
I've had the Sony XM2 and have XM5 both were very comfy.
Especially as I wear glasses and neither become uncomfortable pressing my ears into my frames.
The XM5 are much lighter weight too.
The issue you’ll run into I think is fatigue vs price. The more expensive ones tend to do noise canceling a lot gentler. Also, over-ear will be way better than the earbud-style design for both noise canceling and comfort (therefore, not so small).
I’ve had a great experience with the Bose QCs — Costco has them, so you can save a little money there. Case is about the size of a Kindle if it was 3” thick, and it comes with a wired option.
Seconding Bose, excellent and comfortable.
I used my Sennheiser True Momentum 4s on a 14+ hour flight, they were very comfortable and the noise cancelling was excellent. Battery lasted for about 8-9 hours.