My A40s eventually became worn out so I did some research, got some opinions, and eventually landed on these.
They are a little outside of your budget but they go on sale every now and then. They are super light - I mean they weight nothing compared to my A40s, but they are durable as hell.
They do indeed work with the Mixamp.
Most headphones/headsets should work fine. Just make sure you enable Windows Sonic or Dolby Atmos. I have quite a few different sets I use but my favorite are the Sennheiser Game Ones.
Sennheiser GameOne headsets are nice, open back, and a super cushy velour pads. You can wear them all day with zero discomfort, By far the most comfortable gaming headsets I've worn.
I wouldn't pay full retail or even close for them though. I got them for 120 at Microcenter with a Amazon price match the prices fluctuate a lot it seems.
As for a monitor. Get the Acer XG270HU if you have an AMD Card. The monitor is 144Hz, 1440p, 27" and it has Freesync. You can probably find it for around 300 if you shop around, or wait for sales. 390 on Amazon ATM. The only drawback to it is it has no fucking VESA. The stand is nice though and minimal, there are DIY guides online to make it VESA.