Basically what ohnoitsabear said.
If you're on a budget, build it yourself. You can buy a premade, its ALWAYS a relative waste of money. As an example I finished building what was, at that point, my current rig [It still is my current rig, but I've added a ton to it] a couple of years back. It cost me $1250 for massive overkill. Alienware send me an email; basically the same rig I built, with a bit more harddrive space and a worse CPU for $3.8K. And that's normal. Alienware are among the worst [Apparently there are other companies that are as bad in America, thankfully I haven't seen them here down under], but they also have some of the better performing machines.
Build it yourself and you'll get better performance, and a lower cost. This should be your first choice assuming you are able to, and are willing to go to places like www.overclock.net or other dedicated PC building enthusiast sites and asking for help on how to do so.
Whether you decide to buy premade or build yourself though, always go for an i5 processor by Intel. Don't know the AMD equivalent, they're cheaper, but personally I don't like them. There are people that like them and don't like Intel, so take whatever you like. Intel is more expensive, IMO has easier naming conventions [i3, i5, i7. Guess which is the most powerful and the least], and in my experience are more reliable. The highest CPU you'll want to be looking at is an i5 3570. Do not buy anything with a K on the end. That just means its overclockable, which is not something you'll need and costs extra money. An i5 2500K is good as well. Dependent on how much you want to skimp you can game fairly well on some i3s, but you'll want to ask specifically what they are as most i3s are built for more Internet, Movies and Photos stuff.
RAM you will not need more than 8Gb. Well, you might if you leave every window you ever open open like my sister does, but 12Gb is what I have and its excessive. 8Gb is more than any game will require by itself, covers windows, and'll still give you 2-3Gb to spare for Internet, Antivirus, and whatever else you might want to run whilst gaming.
Motherboard... If you're building yourself ask for a build and take the motherboard given in that build, otherwise don't worry about it. Buying premade its not something you'll need to worry about - enthusiasts will look at them and go "That's crap, that's ok, that's great", but being able to tell the difference is something you're unlikely to want to bother with, and there isn't a ton of difference most of the time anyway.
Power Supply is similar, just make sure its from a reputable brand and not anything that sounds Russian or Asian - companies with those sorts of names generally give powersupplies that'll die and kill your whole system if you're not lucky. Can get some that work, but its like going to a casino and trying to win money.
Graphics Cards... You'll want at least a 560Ti. It is better than a 650 according to my Internet research. If you still have money left over, go for a 660Ti instead. If you STILL have money left over go for a 670. Anything higher and your wasting your money unless you have 3 screens at 1440p [Exaggeration sure, but you won't need it]. Also, that's for Nvidia cards. Again there is another brand, Radeon, that are cheaper. They can offer better performance per dollar, and in some ranges their cards outperform Nvidia ones [Though the difference in outpeformance is negligible for both companies], but I don't like them. Some do and prefer them to Nvidia, I don't, and everyone admits their drivers are a mess.
After that you shouldn't need to bother with a screen if you have a TV, and hopefully you've got a mouse and keyboard already.
Solid State Drives [SSD]s you'll want to stay away from unless you have a lot of extra money to buy a reliable one from a good brand, and really value loading Windows in a couple of seconds [3-5 instead of 30-60]. Otherwise there is no benefit 99% of the time.
If you're looking for a build to build yourself, I'll give you a skeletal outline here that I or others can research and flesh out more if you're interested;
CPU: Intel i5 3570
Graphics Card: Nvidia 660Ti
Motherboard: ASROCK Z77 Extreme4 [Some people don't recommend ASROCK, some do. Your choice as to whether to take this or the P8Z77 though]
RAM: 8Gb. Shouldn't matter too much the brand. Preferably 1600Mhz, 1333Mhz is fine too.
Hard Drive: Seagate Barracuda 1Tb
Power Supply: Seasonic S12II 520W Bronze Certified [Around 500-600W should be fine, brand doesn't matter too much so long as its reputable]
Case: NZXT Tempest 410
Other than that there's the cost of Windows 7, Cost of monitor, Cost of KB+M. For what's listed though, that should come to about $900 or so. Could search for cheaper or more expensive dependent on what you'd want, and actually refine the list a bit better seeing as I mostly just grabbed them off logical increments 'cause you're not yet sure if you want to build one.
