$500 with monitor and OS is a bit tricky, but since gaming performance is a secondary concern, it's possible.
I could get this below $500, but: Pink case. Pink keyboard. Pink mouse.
PCPartPicker part list / Price breakdown by merchant
| Type | Item | Price |
|---|---|---|
| CPU | AMD A8-7600 3.1GHz Quad-Core Processor | $79.99 @ Amazon |
| Motherboard | ASRock FM2A88M PRO3+ Micro ATX FM2+ Motherboard | $52.38 @ Newegg |
| Memory | Mushkin Stealth 8GB (2 x 4GB) DDR3-2133 Memory | $41.99 @ Newegg |
| Storage | Hitachi Ultrastar 750GB 3.5" 7200RPM Internal Hard Drive | $34.99 @ Amazon |
| Case | Apevia X-QPACK3-PK MicroATX Mini Tower Case | $59.99 @ Amazon |
| Power Supply | Corsair Builder 430W 80+ Bronze Certified ATX Power Supply | $15.99 @ Newegg |
| Operating System | Microsoft Windows 8.1 OEM (64-bit) | $94.95 @ B&H |
| Monitor | Asus VS228NL-P 60Hz 21.5" Monitor | $89.99 @ Newegg |
| Keyboard | AZIO HUE Wireless Slim Keyboard w/Optical Mouse | $29.99 @ Amazon |
| Speakers | Logitech S120 2.3W 2ch Speakers | $15.49 @ Amazon |
| Prices include shipping, taxes, rebates, and discounts | ||
| Total (before mail-in rebates) | $545.75 | |
| Mail-in rebates | -$30.00 | |
| Total | $515.75 | |
| Generated by PCPartPicker 2015-11-14 13:50 EST-0500 |
Cost without Pink Case: $503.36 - $12 Promo - $30MIR + $1.99 Shipping = $463.35 (reason its that much cheaper is that the Pink case has USB3 on the front, and as you'd generally want to use those, it needs a $10 more expensive motherboard.)
Only other real place to save money would be on the monitor, and something to consider would be finding a Goodwill that has computer parts and picking up a Monitor from them. They're usually $15-40 there and while they aren't the greatest monitor, you don't quite need the greatest either. - Newegg also has some cheap monitors, but those are typically refurbished (which, again, in this case isn't quite an issue so long as its functional, the bigger problem is that they're often 1280x1024), for example there's Refurbished Lenovo 1440x900, $43