He asked for a build for LoL. On this premise he could get away with a ~$500 build and max the game easily.
CPU: G3258
Motherboard: H81 with BIOS that can support the g3258
Ram: 4GB
Storage: 1TB
Case: Corsair 200R
GPU: R7 260
PSU: Any decent PSU 300W and above
OS: 8.1