I5 12400f is one of the best budget gaming CPU along with 12100f and 5600. High end gaming PC should get intel 13th gen or AMD 7000 series, or at least 5800x3D if you already have AM4 mb.
Warning: no build-in graphics
Might able to get free Game (or might not): Call of Duty®: Modern Warfare® II Standard Edition https://softwareoffer.intel.com/Campaign/LearnMore/18d45e50-…
$20 cheaper than the next cheapest price on Part Picker AU