Im afraid your budget is too low for a gaming ring in that price range.
Usually, for a gaming Rig that plays well in multiplayer+recording you need an expensive CPU.
I suggest you save up till at least 800 Dollars (equivalent) before trying.
Remmber that if you get a PC that is okish in everything, changeing one part later for a good componenet wont make your PC perform Good, since other componenets will still be holding it back.