PC Build

Depends on if you care at all about aesthetics. If you go for cheapest possible case, stock cpu cooler you can get something like a ryzen 5 2600 with nice GPU. For gaming my advice is to spend about half your budget on the GPU since it's going to have the biggest impact in your frames by far.

If a monitor is included in that budget then things get a little trickier becuase now you're balancing power levels so that you get a GPU that's sized right for your monitor

I think a 2070 Super is probably doable with that budget if a you don't need a monitor (already have one or plan to connect the PC to you TV)

One really cool thing about have a badass pc is that you can use Steam in home streaming with a cheap $25-40 bluetooth controller on your phone and turn your phone into a beast of a gaming 'PC'