Recommended requirements for League of Legends is: CPU Speed: 3 GHz processor; RAM: 2 GB of RAM (Windows Vista and 7 users should use 4 GB of RAM or more.) OS: Windows XP SP2, Windows Vista SP1, or Windows 7; Video Card: GeForce 8800 or equivalent video card (Dedicated GPU with 512MB+ Video Memory(VRAM))
Recommended requirements for Minecraft: CPU 3 Ghz, 1 gb ram, GeForce 8600 GS
Compare what you have now to what is recommended and you will know what you will need to buy. If you can afford a new computer that would be best.
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