Well this took some work! I'm not by any means wealthy, and between various responsibilities I don't get much spending money, so I decided to build the best computer I could for less than $400 including shipping, and I believe I've done that!
I bought the CPU on sale from Fry's, the motherboard on sale from Newegg, I had the hard drive from a previous build I had to sell to help with bills, the ram seems to be newly released and is great value, I bought the PSU from EVGA's b-stock, and the GPU was bought from /r/hardwareswap (shoutout to /u/dringus_khan!).
The case isn't the original one I had in mind, however. That's an adventure of its own. Long story short Tiger Direct is out of business for a reason. The case I did end up getting works great, though, especially for its price. I bought fan for the back of it, however it hasn't arrived yet. The only thing I'd like to have done is get an SSD and get a new HDD, but I can add those in at a later date once I have $70-$80 to throw at them.
I could have spent less on the motherboard, but I didn't want to fully cheap out on it, and I wanted USB 3.0 headers. At the time PCPP was telling me it wouldn't be compatible with my CPU, but I didn't see how that was possible, and when it went on sale I jumped on it anyway. Even so, I was nervous the entire time until the screen lit up!
It runs great! The GPU does run a little hot but not enough to be worried about . All in all I'm very happy with how it turned out, and all for more than $100 less than I had sold my previous computer for. Funnily enough it's even faster than my old one, so I guess all's well that ends well.
I built this to play Fallout 4 (once I can actually afford it) and other RPGs, as well as FPSs and MMOs. It'll get a lot of use in the future!
Ps. The lamp isn't actually there, it's on my desk now.