For monitors, you can get some very good headsets suitable for PC gaming..... in so far as sound quality and frequency response. However, the microphones are not really as good at reproducing the kind of recording quality as you can get from a good dynamic microphone. So it does come down to what your pocketbook can support, and how good a recording you are wanting.
Somewhere around these forums there was a discussion about reasonably priced microphones (for voice and/or instruments) you might search. Or just do what I did and get a Blue Snowball (USB) mic, and a gaming headset (just don't bother plugging in the mic cable). It will let you monitor what you are doing in real time and capture a good quality audio signal to feed to your DAW. Around the house, that combo will certainly get you by without breaking the bank. In a "live" or studio setting..... yeah you'd really want to step up to some high quality gear, which may include "specialty mics" designed specifically for instruments or vocals. Not saying that "Blue" is not top quality gear, you get a lot of "bang for your buck" with a Snowball.
"what is this quintessence of dust?" - Shakespeare