It will run Skyrim and just about everything else maxed out on a 1080p monitor. Do you have any particular needs for the KB and mouse? Myself i'd go for a full size mechanical KB with backlit keys (~$100 depending on model) and something probably the Razer DeathAdder mouse (~$60).
Personally I would add those onto the budget and if I couldn't afford them now just get a cheapy kb and mouse combo to tide me over till I save some more, but let me know if you want me to make a build for $1000 with peripherals included and if you have any requirements (backlit, tenkeyless etc).