Microphones for your singing
You're going to want a stage condenser mic for your performing, despite what people say and everything you read. That is my opinion as of the technology today. And you will want a different condenser mic, a recording condenser mic, for your recording.
The common thought is that dynamic mics are more robust and durable, and that condenser mics will create feedback. Though condenser mics might be more sensitive, it seems marginal. Live condenser mics are made to be on stage. You'll be a much happier singer, even if the audio engineer, whether you have a whole sound crew or it's just you, might have a few more things to tend to, like the fact that a dynamic mic is a plug-in-and-sing mic, whereas the condenser mic needs phantom power which is enabled with a button on your mixer.
Though you need to try out microphones to find the one you like the best for your voice, we use Sennheiser e965. Before that my constant companion was a Shure Beta 87A, which is also a live condenser mic, by now a bit older, but also a superb mic. Both offers brilliance and accuracy. The Sennheiser e965 feels bigger and more profound, both to hold, to sing through and to listen to. But both are worlds away from the dynamic mics.
If you go somewhere and there are Shure SM58 mics for your singing, be aware. You do not want that. Though a very recognizable mic that has been around for a very long time, used for many things, they are not your friend if you are a singer. They are dynamic mics, that you will need to have your mouth on the whole time for it to pick up your voice, and you will still be risking straining to be heard. You feel like you sing into a pillow.
Condenser mics on the other hand feel like your voice got lifted up on to a pedestal and all the lights came on. Your voice is magnified.
Condenser mics help you be a better singer because you can hear yourself - whatever you put in you can hear come out amplified, versus the dynamic mic unfortunately, that can risk making you be a less good singer, because you might have a hard time hearing yourself back the way you thought you sang, and in turn you might start straining, which basically is the same as yelling and screaming.