In terms of headphones, I know that the Behringer DT 770s and 990s are an extremely popular option among people.
As far as microphone goes, I'd assume you'd be wanting a USB mic so that you don't have to purchase a separate audio interface, if that is the case there's a lot of really good USB mics available. Just to mention a few, Elgato Wave 3, Blue Yeti, HyperX Quadcast, Rode NT-USB or Shure MV7. If you were, however, wanting to get an XLR mic there's a lot of fairly cheap audio interfaces that would do the job. I think the most common would likely be the Focusrite Scarlett Solo 3rd gen as it's relatively cheap and has a solid reputation as well as very clean pre-amps. Then as far as an XLR mic goes there's 100s of options, based off the budget idea, the AT2020 (as someone else pointed out above) is a solid mic and has clean quality and it really won't set you back all that much. Another alternative to the AT2020 is the Rode Podmic which retails at relatively the same price.
Anyway, hope this helps.