I was just about to ask if there’s an update! Good to know we’ll be able to hear this track soon!
In case you missed it, here’s one really good software you can use to rip the track from the DVD https://www.fosshub.com/Exact-Audio-Copy.html
To be honest, for a beginner any condenser mic will do the job. There are $50-80 ones that will do perfectly for the time being. For example this one I've used for a couple of years now. My advice is to look up reviews on YouTube so you can hear the quality of the sound yourself before you buy. Good luck with your covers!