Graphics Cards (help please)

Hey,

I'm looking to get a new computer and I was wondering what a good graphics card would be to use. I will definitely have the processor and the ram but on the graphics card I'm lost. I will most likely be custom building so I will probably have good options to do exactly what I want. Here's my question, What graphics card could I get to run League of Legends at Ulta High setting and shadows; just maximum possible settings. At a minimum of 120 fps? I have a fairly high budget but I just want to get AT LEST the mentioned criteria for the cheapest price. (max settings, 120 fps!)

Thanks a Million!!