Even with an AMD A6, 300$ (USD?) is pushing it. It should handle LoL okay, and you should be able to play CS:GO at best at medium settings. It should be smooth though.
The A6 processor is not a good choice for gaming atm. It cannot play any current titles at high graphics and it will not be future proof in any way. Any reason for the A6 being the only available CPU? Can you not order another online with the rest of the parts?
Even with an AMD A6, 300$ (USD?) is pushing it. It should handle LoL okay, and you should be able to play CS:GO at best at medium settings. It should be smooth though.