I record some of my own music at home, including singing. The microphone I'm using is not very good (it's a essentially a podcast microphone, some reviews explicitly say that it's not really suited for recording a singer) and I thought about getting a better one. Now the room I'm recording in isn't exactly a professional studio either, it's just a normal living room that is not sound treated in any way. Does it even make sense to spend money on a better microphone under these circumstances, or would that not help much if my room doesn't have good acoustics?
Room acoustics is indeed a very important and often underestimated component of good recordings. However, that doesn't mean microphone quality is less relevant. It's impossible to say which of the two is more important – in some recording scenarios, you need both a good room and a good mic. In others, a good mic can largely make up for a bad room. And in yet others, neither the room nor the microphone actually matters so long as you know how to compensate.
Also, microphones don't simply rank from “good” to “bad”, but there are different types. Some of them work well for almost everything. Some are crazy expensive and great for some particular sources, but should not be used for anything else. On the flip side, there are dirt-cheap mics that still do the job just fine for some instruments.
Similar story for rooms, but perhaps even more extreme: some rooms have acoustics that work excellent – at least for some kinds of music – despite not being designed with music in mind at all, let alone recording. Others are a complete disaster even with expensive acoustic treatment.
Ok, that was really just an extended comment. What gives?
I'd suggest you get a microphone, based on what you intend to record, and completely independent on what room you plan to record in. Don't buy a crazy expensive one, just one that you can rely on to work reasonably well. A good strategy tends to be to start with the cheap house brands of well-reputed music stores. Even better if you can get a couple of different types. Unlike on Amazon/Alibaba etc., it's unlikely that you'll get something completely useless, and even if it's too bad for what you need right now it might still come in handy at some point in the future when you need to record a bunch of other instruments.
But the first thing mics will allow you to do is better judge how good the room is. Even if it turns out the room is so bad that the recordings come out useless with both mics, mics are not a wasted investment: you can add acoustic treatment later on, and/or in the meantime record in other rooms. And practice, and learn what things work well with which microphone.
Really, that's the most important thing: you need to learn what you need to obtain such and such result. The best room, best mics and best gear are utterly useless without a recording engineer (“quoting fingers”) who knows what they're doing, just like the best instruments are useless without a musician who can play them well. Having a microphone other than a simple podcasting one is very useful for that learning.
Yes, not despite, but especially because of your bad room acoustics. There are big differences between microphones in how much of the room sound they pick up. I would recommend a microphone with a rather tight pickup pattern, with high off-axis rejection. Don't expect to achieve a very high audio quality without addressing room accoustics though.
Podcasts need clear, intelligible speech. Singers like to be flattered! Sometimes singers like to 'work the microphone', pull back for the loud notes, go in close for a bit of intimate bass-boost.
You don't necessarily need a BETTER, more expensive microphone. Maybe you could use a more appropriate one.
A 'normal living room' with carpets, bookshelves, soft furnishings etc. might actually not be acoustically that bad at all! The big problems come with SMALL rooms, which are unfortunately all many people allow themselves as a studio.
Certainly! Using a mic with a cardioid pick up pattern, close to the vocalist's mouth, you're not going to record that much of the room acoustics. The Hz range of such a mic will be wider than the podcast as well, being able to capture more than the podcast mic's.
If you're recording guitar, for example, you'll put the mic right in front of the speaker, so the room's acoustics won't come into it either. That, or D.I. the guitar, and use the effects available.
So, unless you're going to record with the mic a few feet away from the sound source, the room's acoustics are pretty well immaterial. They would probably have more bearing on the speakers you listen to playback through!
The better the mic, the more it's going to capture, so go for it. Be it a dynamic, or better still, a condenser mic, more expensive for that very reason.