TLDR: A 120W if you intend to keep the 5600g at stock.
Its tdp is 65W on paper, but its 'package' power is about 80W. Thats the extra power for running the rest of its connectivity with the motherboard. It includes the combination of both CPU and GPU. Most other things use little power, but would add up if you connect a lot of stuff. This could be fans and drives, game controllers, external USB stuff. The memory will be about 5 or 6 watts usually.
Not running any case fans (no need for them at this power level), just 2 sticks of memory, keyboard, mouse, sometimes game controller. I haven't been able to exceed 80W at the wall. So a 120W would be fine for what you describe.
I measured the performance of my 5600g at stock and at the usual 45 watt (60 package) eco mode. The usual undervolt to 5000 series applied and the 10% gfx overclock that most motherboards will offer. I could not find a difference in gaming performance. And video editing wasn't too badly affected if I recall. I run it at this setting on a pico psu (the absolute bobs basic cheapest one you can find) and a 90 watt power brick. Power bricks all tend to be 90% (silver) efficiency. The will not be more efficient even at these low loads than very recent big gold class PC PSUs with recent more 'square' efficiency distribution curves. But they are not bad.
