Considering that you'll be building quite far down the road, I'd say post again for help about 2-3 weeks before your intended build time. Prices fluctuate quite frequently in the PC world, so any build posted now won't be as relevant.
However, this build should give you a ballpark about what to expect performance wise.
PCPartPicker part list / Price breakdown by merchant
| Type | Item | Price |
|---|---|---|
| CPU | Intel Core i3-4150 3.5GHz Dual-Core Processor | $104.95 @ SuperBiiz |
| Motherboard | ASRock H97M Anniversary Micro ATX LGA1150 Motherboard | $60.98 @ Newegg |
| Memory | *Team Elite 8GB (1 x 8GB) DDR3-1600 Memory | $49.99 @ Newegg |
| Storage | *Western Digital RE3 1TB 3.5" 7200RPM Internal Hard Drive | $44.25 @ Amazon |
| Video Card | Sapphire Radeon R9 280 3GB Dual-X Video Card | $164.99 @ Newegg |
| Case | Cooler Master N200 MicroATX Mid Tower Case | $39.99 @ NCIX US |
| Power Supply | Corsair CX 500W 80+ Bronze Certified Semi-Modular ATX Power Supply | $39.99 @ Newegg |
| Prices include shipping, taxes, rebates, and discounts | ||
| Total (before mail-in rebates) | $545.14 | |
| Mail-in rebates | -$40.00 | |
| Total | $505.14 | |
| *Lowest price parts chosen from parametric criteria | ||
| Generated by PCPartPicker 2015-04-02 15:11 EDT-0400 |
An SSD is pretty low on a $500 gaming PC's priorities, so I couldn't include it without a significant sacrifice for your in-game performance. For 1080p gaming, the 280 should perform respectfully and is more than enough performance for League and CS:GO.