In contrast to CPU’s which seem to last for ever, I’ve had many graphics cards die on me. Integrated graphics suck for gaming, but it’s better than nothing, and it’s a lot easier to switch over to the iGPU than it is to swap out a PCIe card in order to diagnose a problem.
My point: get a K instead of a KF.
Also, regarding the cooler, If you run the chip within Intel’s official specs, you lose something like 3% performance, but it uses about half the power. Point being, you don’t need that cooler. I’m in a similar situation (my PC was build Summer 2013) and picked out a https://pcpartpicker.com/product/MrvD4D/ek-nucleus-aio-cr360-dark-72-cfm-liquid-cpu-cooler-3831109900178
Yeah, I don’t want my computer turning my office into a disco. It’s surprisingly difficult finding parts at anything but the lowest price point that don’t light up a room.