I'm about to purchase a AT2020 studio mic, trying to save $47 I'm getting the XLR version. If I use a XLR to 1/4 converter then use a 1/4 to 1/8 adapter on top of that and plug it into the pc, will it work?
That mic needs phantom power so no it won't work. You'll have to buy an interface. Why don't you rather get a USB mic instead? The quality is just fine for home studio purposes.
If you're set on an XLR mic then you'll need an interface. The focusrite scarlett 2i2 is a very high quality and relatively cheap interface with very low latency. It also sports phantom power for your XLR mic.
Note: The USB mic's don't require phantom power so you could just plug it into your pc directly.
And if you buy just the Phantom Power Supply then you will need an extra XLR male to 1/8" cable. Just search it on Amazon and buy the one that is the right length for you.