the best option would be to go with a AMD A8-6600k, this will run League of legends at medium to high at 60fps.
you could get the MSI FM2-A55M-E33 motherboard for about 43 euros with that.
then you just have to get 8 gb of ram, a case, a powersupply of 400 watts minimum, and if you want one, a dvd drive.