6 essential parts to a PC required for gaming (7 with the case). They are:
CPU
motherboard
GPU
Data drive
System memory (ram)
Power supply
The CPU is responsible for dynamic calculations and processes. Basically things you change and the PC can't predict. So opening a movie for instance, or transferring a file. The PC didn't know you would do that, so it has to dynamically display the video or transfer the file. The speed of the CPU determines the speed at which these events occur. The faster the CPU (the higher the GHZ), the more fluidly and quickly random events play out. The more cores a CPU has means that higher number of events can play out at once.
Motherboards are the central hub. It connects everything together from video, sound, mouse, keyboard etc. Everything routes through the motherboard. Most these days are very inexpensive and very feature rich. Don't have to worry too much about the quality of this part, even though its so important.
The GPU is by far the MOST important part of any gaming PC, and by far the most expensive. GPU's are responsible for handling massive amounts of video memory and calculating physics within games. The more video memory you have, the more information (more detail and textures) you can display at one time. The faster that video memory is clocked will determine the rate the information is displayed (referred to as frames per second). So you need both large amounts of video memory, and a high clock speed for a GPU.
The data drive stores all your games, movies and files. It HAS to be a solid state drive as a boot up (the one you load your operating system onto). Any extra storage thereafter can be had with cheaper Hard disk drives.
The ram is the least important aspect of a PC. Having more ram (system memory) will simply allow you to keep more programs open at one time. Like the internet open with a video playing, while you chat on Skype and download a video, etc. The more ram, the more you can do at one time. 8 GB of system ram is more than adequate. You can go up to 32Gb if you wish, it will not benefit gaming in the least.
The power supply is important, but not as much. You just want to have one that is at least 500W. Anything in the 750w range will almost always suffice.
That's it, a PC. Now for gaming you really should be operating on a Windows based system. Windows 7 64 bit is the best and most reliable. Avoid Mac and Linux for gaming.
There are two main PC contenders. Intel and AMD. They have been neck in neck for years now. Intel always has the advantage, but now it is such a little advantage that AMD is such a better deal at its lower price point. So yes Intel is the king of PC, but AMD is far more economical. So that being said, I am going to suggest an AMD build for your first setup:
Cpu: AMD Fx-8350 ($200)
Motherboard: Gigabyte 990Fxa-Ud3 ($150)
GPU: Gigabyte HD 7950 (~$280, with free games)
Data drive: Intel 120gb SSD ($100)
Power Supply: 500W + (~$60-80)
Ram: 8gb DDR3 (~$30-60)
Case: Zalman Z11+ (~$55)
Total cost: ~$900
Now that may seem like a lot compared to a console cost. But if you have never gamed on a PC that can crank all settings to maximum you have no idea what games can look and play like on a system like this one. The games compared to console version look so smooth and beautiful words can't describe it. It is literally jaw dropping to play a game on a console, and then view it at maximum settings at 60+ fps on a PC. It isn't even the same game at that point.
Honestly $900 is a MODEST gaming PC price. You will NOT beat this setup at $900. If you have the cash, and you want the best of the best...
I7-3970x
Nvidia GTX 690
Gigabyte GA-Z77x-UP7
Dominator GT 32 GB 1866Mhz
1000W power supply
Intel 480Gb 520 series SSD
$300+ case
Total cost: ~$3000-4000
You can also add 3 more GTX 690's, jumping the price to about $6000-7000.