computer build help

Hi, I've been playing League on a laptop for quite a while, but recently a friend of mine gave me some parts he didn't need to build a desktop. I've searched this quite a bit and the answers are all over the place, but I'm just trying to figure out what I need to play League at 120 FPS on 1080p (since that's what my external monitor is). In regards to other games, occasionally I'll play some WoW for a patch or two, and I'll probably pick up Warcraft 3 remastered when it drops. I think both of those don't have very high requirements to play at 120 either. I have no intentions to stream anything, or do any work requiring just a whole lot of power (I have a work computer for that). Would like to note as well that I'm not looking to future proof this thing for any amount of time. I'm just trying to find out the minimum requirements to run 120fps at 1080p. The parts he gave me: Some flashy looking computer case MSI MPG Pro Carbon AC Motherboars 16 GB (2x8 GB) 3000 Mhz Ram 500GB Samsung Evo Nvme M2 SSD 500w Corsair power supply So basically I think I'm just looking at the processor and motherboard. I found the i5 9400F processor for like 120 bucks, which seems fine. However, what graphics card would I need? And would the i5 be enough for 120 FPS? Any help would be appreciated, I'm just trying to throw the other parts in for cheap. Hoping there is a card under 200 bucks that can do what I need. Thank you for any help!
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