sE Electronics - X1 R

It sounds like you only have 1 mic/1 input available at any given time. The part I don't like about that is that you might be missing out on the possibility of a stereo image on the piano. If you were to ask me(and probably ONLY me), I'd say 2 of those Beta 58s or even the Beta 87s would be just fine on a piano, BUT YES... it WOULD pick up a lot of the clack and clunk from the keys.... however, some people like that. Even if you only had 1 mic for the piano, those Betas sound pretty good. If you are looking for an upgrade on mics that will give you a studio sound with less "condenser" sensitivity, I would recommend Ribbon Mics like the sE Electronics X1R. These mics are not too expensive at all, and they sound like a dream (especially for how inexpensive they are). However, they are definitely not as "bright" as a condenser mic. The other thing I'd say is that even a standard SM58 sounds decent for vocals in a studio setting, however if it is true that you only have the one input, then regardless of mic choice; I'd recommend recording the piano first AND THEN the vocals. I certainly would not recommend using a single mic to record both the vocals AND the piano at the same time. As for the other mics you mentioned... The SM7b is AWESOME on female vocals, but it IS pretty pricey even for how good it sounds(at least in my opinion) and the Rode NT1 is simply a horrible choice all together. I'd rather one of the Betas on a piano before the NT1. You'd definitely be better off with a Ribbon mic (or 2, since you should be going for stereo image anyway) OR even an NT5 before that NT1. In any case.... Those fluid performances CAN still be recorded independently from each other, especially if you are like me because I cannot fathom doing an entire performance without a click for at least the main portion of it.

If you need to cater for both guttural and crazy highs you might be better off going for two different mics (used), since I don't think any mic in your budget would handle both in a great way. I would drop 50 bucks on a 57 and the rest on one of the budget ribbon like the sE X1 R. The ribbon should work nice on the high vocals provided that the singer isn't ridiculously loud and that your room doesn't sound bad (the figure of 8 polar pattern will pick up a lot of room sound). Otherwise I would still go for the used 57, which will anyhow do the trick, and save 150 bucks which will get you one third of the way to an SM7b!

The SM58 is an incredible mic that will last a long time but is better for singing live than recording in my opinion. The Audio Technica 2020 or the sE X1 for the same price are condenser mics and great for recording vocals but also acoustic guitars and lots of other things. Assuming you have an audio interface to plug an XLR cable into those are great mics for recording vocals!

Another vote for sE here - I have the x1 and V7; both excellent mics for the money - though I'm not sure I'd compare them to Neumanns!. I also have the Rode NT1, which is another fantastic device at the price.