Im going to mainly use the gaming pc to play bf3, crisis 3, bioshock infinite, dota 2 and so on. I have to at least play them at 1080p on high settings. My budget is $750 and i have all the mouse, keyboard, os and monitor.
To be honest youd be best off aiming at an AMD set up for that amount of money, it will save you to cash to be able to afford a better RAM setup and GPU.
The AMD A10 5800k is a good chip for its price, with an equivalent motherboard. Im sure you could find a bundle that would make it worth your while.
Get 8GB of DDR3 1600mhz RAM, this is the best price point at the moment, but dont buy more expensive ram like Corsair Vengeance just cos it looks cool.. its better to save money here for getting a better GPU.
Power supply.. well youll want somthing along the lines of a Corsair CX500M or a 430W CXM , definately get a modular power supply, You wont be running excessive parts for a non modular and they make one of the biggest differences to lots of junk in your case.
HDD: its up to you really. you can save money on this quite easily, just dont go for a dud make. I can let you find this yourself quite easily. Even going on amazon it is very clear that some makes are very often D.O.A , obviously avoid them.. you tailor that to your need. You may not even need 1TB.. thats alot of freekin memory for a casual gamer.. and dont forget that you can always buy more drives in the future..
Cases.. there are some beutiful cases around atm.. from micro ATX to full sized ones! Recently did a build for my dad with a Bitfenix Prodigy, theyre very good looking. But if you want a full build something like a zalman Z11 plus or a Cooler Master HAF 912 - (i quite like this one). just take a look :http://www.overclock.net/t/1326537/cases-for-modding
GPU: decide this last, try to get components as cheap as possible by reputable makers! honestly an hour spent on the internet can save you well over $100 on parts..
By the way, dont go by what ive said or what anyone else says. Thats only one possibility mate. Try and learn abit about what different parts do what and this means you can tailor the PC to what you need out of it.. Search these forums and have a look around the intenet at other forums, look at reviews of products before you buy them and buy only when your confident the parts have exactly what you want!