I assume you meant that you needed os and monitor in addition to the parts
How much higher budget? Its late so I didnt have much time to put into it and as a result went $200 over budget, but some of those parts would be a good start, like processor, ram, hard drive; motherboard is also good too. The power source is a nice but cheap one and is big enough to support SLI (2 GPU at once) should you ever decide to do so). I dont really know how intense your games are but that gpu is a cool-running gpu that can play at least skyrim on good settings. The aftermarket cooler is optional for overclocking, get rid of it if you dont want as cpu comes with a stock cooler. The optical drive is also optional as you can do a lot of stuff with USB/steam/etc. the case is more up to you, i just picked one that i remember had good reviews, fractal r4 is another good option. I dont know that monitor in particular but i got an acer for that price a while ago and it still works great. Windows 8 or 7, they both cost the same. Consider an AMD cpu if you want to shave off more $$ (will need to change the motherboard as it is a different cpu socket). Could use more case fans or experiment with aftermarket coolers/liquid cooling to stay cool. A case with good airflow and parts that stay cool (like that gpu) also help And finally, check around and do some of your own research, i figured out my cpu was $30 cheaper at microcenter than amazon with just a little Googeling
Im going to assume you want overclocking potential for this, if not just switch out the processor to a non-K version (its like 5 dollars difference on Amazon right now)
http://pcpartpicker.com/p/1meMV
Assume the total price is a bit lower as different sites have different deals that partpicker doesnt always catch.