I can agree with everything said so far, at least the parts that I have personally experienced.
DT-770-80 is a solid headphone and almost indestructible, plus Beyerdynamics replacement parts are great
NTH-100 is amazing and sounds great without a dac/amp and Rode will 100% stand behind their product, a pleasure to deal with them (has an optional M variant with a mic and TRRS cable)
IEM's are great but might pick up system noise but with how cheap they are you could get a baby dac/amp that'll be cleaner
I would look at some other Beyerdynamic's like the Tygr and MMX300
AKG K361 is a great headphone but the stock pads are a little slim, easy enough to get thick plush oval pads for. The build quality isn't the highest, a little creeky but durable.
Sennheiser offers a ton of excellent headphones, however I'm a snob with mine and if it's not a clean dac and powerful amp I don't want to listen to them, or tubes lol.
I would out of best practices attempt to avoid the TRRS (4-pole 3.5mm) wire if at all possible, I don't hear about people having an issue with it but I always have a problem of output bleeding over to input.
Look at the antlion modmic products, can't remember if that's only in north america this can be found.
Perhaps consider a desk mounted boom arm mic or a blue yeti etc, it'll cost you more in the long run but will avoid what you're dealing with now of throwing it all out when something goes bad.