Should your microphone have character, or should it be neutral?
There is a current trend for microphones to have a particular 'sound' of their own, and microphone preamplifiers too to an extent.
This means that whatever instrument you record, there will be superimposed on the sound of the instrument itself the sound of the microphone.
Is this a good thing?
Yes, it can be. If the instrument, the microphone technique and the sound of the microphone are all working synergistically, then if the result sounds good, then it is good. No problem with that.
However, if in a multitrack recording you go on to use that same microphone for other instruments and voices, then the probability that it is going to be such a happy match on them all is remote. And add to that the fact that now your whole recording is taking on the sonic characteristics of the microphone. I doubt if that would be what you wanted.
So ideally a well-stocked microphone drawer (or even cupboard!) would include 'character' mics that are known to work well with certain instruments, according to your preferences, not something you heard from someone else, or worse still the manufacturer.
Also it would include neutral mics, for when no 'character' mic can be found that is appropriate.
Remember that with a neutral recording, you can always use studio wizardry to color it any way you want later on. With a recording that is already colored, it is very difficult to get back to square one.
Don't forget to check out the DPA microphone range.