How about an I3 3225 with onboard HD4000 graphics. HD4000 is fully capable of playing League at close to max settings in 1920*1080 resolution.
And an I3 will also be much faster in other things and allow you to pair it with a PROPER graphics card like the HD7750/GTX650 and up to play any other game too.
What is your budget? Maybe I can work out a build for you. An i3 shoudl be around the same price as the builds you mentioned.