I want to correct one thing that was said early in this thread about good microphones needing a power supply.
That is not actually the case.
Certain types of mics need power while others don’t and that distinction has nothing to do with quality or cost. Some of the best and most expensive microphones out there are ribbon mics, which will be destroyed in a millisecond if they are connected to a power source.
Dynamic and ribbon microphones don’t need power while condensers do and there are very expensive dynamics and ribbons out there as well as super cheap condensers.
I also record theremin and other electronic instruments direct. I will occasionally mic them if I want the sound to be colored by the amp or the room.
And it’s not cheating to re-amp them. Re-amping is when you record direct and then play it back through a speaker or amp and record that at output with a microphone.
Guitarists do it all the time and it’s a great way to make the recording sound more real and alive.
Anything that gets the sound you want is fair game and there’s no such thing as cheating.
Finally, when choosing a microphone there is no substitute for hands-on experience. If you have access to multiple microphones I would say to try them all out and see what you like.
A good inexpensive dynamic mic is the Shure SM-57 or SM-58. I’ve also used the Shure Beta-87 (for vocals) and it is a good piece of kit.
My current go-to microphones are the Electrovoice/Blue Cardinal and Raven (condenser and dynamic, respectively) as well as the CAD 77-A dynamic.
There are some affordable ribbons being produced by Golden Age Project that I want to try and CAD makes a ribbon version of the 77 that is getting good marks.
Blue also makes the Bluebird and the Spark - both are great affordable condensers. I actually like the Spark better for overall versatility.
An even more affordable option are mics made by MXL.
But, as has been said before, you should get the best equipment you can afford and there is definitely a correlation between price and quality.
I hope this info helps.