Would you be using them on your laptop or desktop (eg Logitech webcams usually have decent mics)?
Do they really need to be headphones or would on-ear/around-ear headsets work too?
I generally have a problem in that all headphones fall out of my ears (there's a pair of foam Shure's that don't as much, but they were like $100 for a wired no-mic headphones, and I usually pair them with a Logitech c930e extra wide angle webcam).
I've recently gotten the much lauded Sony WH-1000XM4, but they are very warm on your ears and you look funny, but per reviews, they are the go-to choice for exactly calls + music + travel (hopefully some day soon, right?). At least they don't fall off my head :)
When at my desk, I still hope to resolve my shotgun mic picking up sounds from the speakers pointing away, but I'll probably need to pad my walls to stop the sound reflecting of walls and sloped ceiling. A man can dream, though!
Don’t try to combine them.
For extra points, use your phone as a webcam.
I like to look at the audio systems that professionals use in broadcast television, and then loo around in that space for creative solutions. The Røde Wireless Go microphone is one such solution (see http://www.rode.com/wireless/wirelessgo ), but that only handles the microphone side. I still have yet to find a good professional grade audio solution for headphones.