there are two ways to reduce noise of external sounds.
A) passive noise isolation. eg, closed cans.
the good? sound quality does not suffer, external noises are muffled. many models to pick from with different signatures.
the bad? closed cans can get hot, isolation is not perfect depending on volumes
B) active noise cancellation. eg, playing opposite audio to counter sounds
the good? done right, counterbalancing sounds cancel out external sound influences
the bad? this cancellation heavily distorts audio giving a rather bad quality compared to regular headphones (opinion). options are also limited on what models have this feature (mostly bose and just a few others)
no headphone has a built in amp, only headsets. that goes against what you seem to want (no mic) and gives you far less options.
it may not have a detachable cable, but the dt770 might be up your alley. i'm not sure what kind of signature you want though (dt770 is v-shaped).
otherwise, any closed can which gets rated decently on isolation would work.. just get one with the kind of signature you want.
iems (deep in ear canal type) are the highest isolation model given they act like earplugs. closed models will isolate even better than closed over-ears and can even reduce low frequencies far better.