Okay, here's a rough build:
PCPartPicker part list / Price breakdown by merchant
| Type | Item | Price |
|---|---|---|
| CPU | Intel Core i5-7500 3.4GHz Quad-Core Processor | $192.33 @ OutletPC |
| Motherboard | Asus STRIX H270F GAMING ATX LGA1151 Motherboard | $139.00 @ B&H |
| Memory | Kingston HyperX Fury Black 16GB (2 x 8GB) DDR4-2133 Memory | $110.33 @ Newegg |
| Storage | Sandisk SSD PLUS 240GB 2.5" Solid State Drive | $74.99 @ Best Buy |
| Storage | Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive | $49.33 @ OutletPC |
| Video Card | EVGA GeForce GTX 1070 8GB SC GAMING ACX 3.0 Black Edition Video Card | $379.99 @ Newegg |
| Case | Corsair 200R ATX Mid Tower Case | $45.98 @ Newegg |
| Power Supply | EVGA SuperNOVA G2 650W 80+ Gold Certified Fully-Modular ATX Power Supply | $88.89 @ OutletPC |
| Operating System | Microsoft Windows 10 Home OEM 64-bit | $88.58 @ OutletPC |
| Monitor | Acer GN246HL 24.0" 1920x1080 144Hz Monitor | $188.99 @ B&H |
| Prices include shipping, taxes, rebates, and discounts | ||
| Total (before mail-in rebates) | $1403.41 | |
| Mail-in rebates | -$45.00 | |
| Total | $1358.41 | |
| Generated by PCPartPicker 2017-03-11 13:28 EST-0500 |
Notes:
For memory, get any memory marked as DDR4-2133. As long as it's from a decent brand, you'll be fine. Anything above 2133 will cost more and you'll have to overclock to see any benefit which you can't do without a z170 motherboard, and anything below will have less performance.
You don't need a CPU cooler since your CPU comes with one
The video card is much better than the RX 480 (not in terms of value, but in terms of raw power). It's quite a lot more expensive, but especially with the 144Hz monitor, there'll be a pretty significant performance difference. You can get any card marked GTX 1070 and it'll be about the same. If you see one marked GTX 1080 that fits your budget, that's even better.
If you want to save a bit more you can get Windows for free if you're a student, or just use a trial version.