Case : SilverStone SST-ML08B
More than enough
Check http://noctua.at/en/products/cpu-cooler-retail
A i3-6320 is not gonna produce much heat to begin with so ...
Yes, 400W is overkill, yoour powerdraw should be about 140W .. a 200W PSU could be sufficient, 250W if you are looking for...