As for as the Lenovo goes if you select the under $500 and then in order of low to high you will run into either Intel HD graphics or Celeron CPU or a lack of Ram or CPU speeds. Ok maybe the ThinkPad E545 for under $350 but it's still not worth it to waste on a laptop to do what he wants it to do. However there all used so even though they've checked it you'll get a very very small warranty and if you want to get a extended warranty then it's gonna cost more. Even still there's gonna be a issue with RAM on that E545.
As far as OP's post about having a very good knowledge of laptops, that might be true but idea of a gaming laptop to play and I quote, "edit video ok an that can run games the most demanding game" says otherwise at a price...