I am interested in a pair of headphones that are portable and have enough noise cancelling to diminish the background noises in a subway or flight. I would love for the headphones to be wireless as I have an iPhone without a 3.5mm headphone jack and would rather not deal with a 3.5mm to lightning adapter. I would also hope that the headphones be "over-ear" or circumaural.
The aesthetic, presence of a microphone, and various audio control functions (volume up/down, skip, etc) are not at all important to me.
I hope to spend no more than $300.
I am unsure where to begin research and how to navigate the vast field of headphones.