If you already have some ddr3 RAM, you could go with haswell, if not, a i3 6300 (or a similar model) paired with a cheapish mobo, 8gb ram and a 950 will get you a lot of fps on max settings. Get a goodish PSU, since that can kill your inteire system. SSDs are pretty cheap now, and if it's LoL only (maybe even a few more games) 250GB are pretty decent.