$20 i don't think can cut it. Not unless yo can settle with an ordinary dynamic mic and plug it into your pc sound card.
But if you would like some decent quality,USB condenser mics are best for recording vocals
Of course what I would suggest is the one I have. CAD u37 USB. Got it from Hung Bros 3rd floor in sim lim. Though one thing to consider before buying this is your room, is it sound proof enough. Or get a Samson USB mics, the lastest still i beleive is the C03U. Don't think have yet the c04u here. All these are USB so these types are the cheapest as you can just plug itto your pc. No need for phamtom power and decent soundcard, you should still have a soundcard though to hear what you record. Any pc these days should already have one lol
the shure mics are even better but, will you plug it into your pc sound card? Not unless your pc already has a decent souncard, then you will also not get the proper results.