This is a subject that makes me glaze over very quickly too. DD wants one for her birthday in July so I have been glazing frequently recently. She uses Zoom for day to day or iPhone but zoom means pulling out the card every time you want to listen back properly to get it onto the computer and the iPhone quality is rubbish.
Basically my understanding is that you decide between a USB mic (links straight into a laptop) and a XLR output mic that has to go through a box which is an amplifier and converter. The box e.g. Scarlett, blu-icicle amplifies the audio and converts it to digital. Then you need some method of fiddling with said recording on the computer which ranges from free apps like garage band or audacity to pay a bit/moderate like Amadeus Lite/Pro or pay a fortune for a studio set up. Another complication is if you want the mic to be a long way in front of your instrument to mimic orchestra audition circumstances or a concert then you need a long lead if you want the computer next to you for convenient play back and that may interfere with your USB signal. Finally headphones to listen through the computer.
As for mics - Audio Technica, Rode, Blue Yeti seem to be popular choices. You tube has a number of techy tragics demonstrating and comparing various models. The other thing is what pattern of recording you want (cardioid is common for a solo instrument but the Blue Yeti is meant to switch between patterns for other set ups).
None of which answers your question but maybe someone here has some experience? I do know of a professional percussionist who uses an audio technical AT4040 cardioid condenser mic with a blue icicle XLR-USB. This is a very pricey mic but they do a cheaper version. I am thinking of hoping for the best and randomly picking between a Rode NT USB or AT 2020 USB.