You're on a college campus. Good place to find someone trying to quickly sell a system. I'd look there first. Also, I've saved a ton of money over the years on used monitors. Just picked up an "as new" ASUS VE247H for $50.
To me, the biggest problem you'll have trying to assemble a system from used parts is time, and I'm not talking about the system build time. I'm talking about the time taken to meet with sellers, the time to keep an eye on the adds, etc., etc.
SO,.....I'm going to assume that you meant uATX, not miniITX. Several of these deals expire tomorrow!
Hard to beat this deal from MC:
AMD Ryzen 5 1600 with Wraith Spire Cooler, Gigabyte B450 AORUS M for $135
Mushkin Enhanced Source 2.5" 1TB SATA III 3D TLC Internal Solid State Drive (SSD) MKNSSDSR1TB for $100
If you're in the "collecting parts" mode, this is hard to pass up
LINK: $42
This RAM
should be okay
LINK: $80 (it's not on the supported list, but that list is short for this motherboard, and I have the very similar Ballistix Sport LT 4GB Single DDR4 2666 on 2 AM4 motherboards without a problem)
You asked for quiet, so that means that going really cheap on the case is a no-no, so this case comes with 3 good fans that should be quiet: $56
Fractal Design Focus G Mini Black MicroATX Mid Tower
That's $413 before OS and GPU (and taxes)
As you can see, it's rather hard to build a nice system under $500. The other thing that comes to mind is that you're really close to being able to pick up a GTX 1070 ($220+) Let's look at a change that could be made.
As
@biffzinker pointed out, there's a great deal on an
500 GB NVMe SSD (that means it's faster than the SSD that I pointed to above) for $58 (deal expires tomorrow) Savings of $42
You could also consider a "throw away" system:
ABS Gaming Desktop NVIDIA GeForce GTX 1050 Ti 4 GB Ryzen 5 1600 (3.20 GHz) 8 GB DDR4 480 GB SSD $550