MXL - 603S

I'd go with a decent cost-friendly condenser mic. I don't know enough about mics to recommend one or the other but I think you'd be looking at maybe $100-200 range. I have two condensers as my drum set overheads and each retails for about $100, for example. Mogami 603 II is the model (I think; can double check that later). These were gifted to me but they work really well for pretty much all of the kit except the bass drum but that's to be expected and doesn't sound like something you're trying to do right now anyway. That said, the SM57 is such a proven workhorse too you can't go wrong with that; different performance parameters but you can adjust for that in how you mic up.

MyDream Mic is the Neumann $4000 but even the MXL condenser I have had for like 10 years works well.

Those are great for shows/touring. But for vocals, you definitely want a condenser. I used the MXL for years, and then I got a VERY good deal on Amazon on a Neumann.

I recommend a cheap condenser (I have an MXL) because it really makes a lot of difference, and the quality of the signal that you have to work downstream begins with a) a good treated recording space and b) a decent microphone.