honestly 800 is kinda hard building a gaming PC. The last two I built for my friend were at least 1100 to 1200. The video card usually eats up a good chunk of your budget. I would assume you would get something like the nvidia 760/770 at least if not higher those are about 200-300 dollars (I'm still running on my 660ti, and due for another video card, I cannot even play evolve!)
So let's break down the prices
Video Card - $300
Motherboard/processor (Using an i5, and using newegg combo prices), about $250
I assume you're gonna need probably 8 gb ram (cuz honestly, they're cheap nowadays and usually come in 8gb) - $60
Powersupply (probably 600w - 800w and they range from 50 - 120 depending on brand) - $50
Also, what is your OS? If you want to play a lot of games, you're most likely going to have to run on Windows (sad, I know, if current gen games came out for Linux on Steam, I would be using Linux). Let's say latest is Win 8/1 which is about $100
Will you be buying a case or you already have one, good ones are about $60-70 and up.
Now this random build I just did will cost you just a little over 800 (if you're lucky). I always go for (or at least try to get the best or near best), and if you prefer using i7 vs i5, or even a better mobo, more powerful PS, and even Video card, you will be if not definitely over $1000.
Edit: I am a total idiot, I forgot about hard drives, depends if you want an ssd or just a regular hdd. An 128 gb ssd will definitely push your budget 900 and up