Guide: How to choose a graphics card

Graphics card is the most important component in gaming computer after processor. To play heavy graphics games you need something better then integrated GPU. Choosing the right graphics card can be difficult, because there are dozens of different video card models and manufactures. Currently there are two companies who dominate the GPU market - AMD (former ATI) and Nvidia. Both have their pros and cons, AMD cards for example don't have PhysX support and often have less stable drivers than Nvidia.
So, how to choose the right one? Comparing the specs is one, but not the best way, much wiser is to read graphics card reviews on hardware sites. Choosing just by memory size will not work, because amount of video memory tells almost nothing about the video card performance. There are plenty low-end graphics cards with large amounts of video memory that are meant for tricking people who don't know much about computer hardware. Manufactures sometimes even load low-end graphics cards with 2GB of video memory. To keep price low they use very slow and cheap memory, so 512MB and 1GB versions are usually faster. Lets take an example, person who is looking for cheap gaming computer finds two almost identical computers with only one difference - graphics card. Both have same price, one has 512MB ATI HD 4670 and other has 1GB ATI HD 5450. In this case you should pick older HD 4670, because it's almost 3 times faster than HD 5450. Bigger model number doesn't mean it's faster, HD 5450 is the weakest card of HD 5000 series and it is up to 10 times slower than fastest card of HD 4000 series - HD 4870 X2.

When buying a video card or gaming PC, follow these 3 tips:
Read reviews, then you know performance differences and features
See graphics card ranking list or hierarchy chart
Don't fall for low-end graphics that are marketed as gaming cards

Guide: How to choose a gaming processor

Processor or CPU (often called brain of the computer) is a important component of gaming computer. There are many CPU's to choose from, with different clock speed, number of cores, different sockets and so on. There are two important processor manufacturers, Intel and AMD. Both companies have wide range of processor models from cheap single-core CPUs to expensive processors with over 6 cores. When you compare Intel and AMD processor's clock speeds then remember, they use different architecture and are not comparable. Remember, different brand processors use different sockets, you cannot mount AMD processor to Intel motherboard or vice versa. You can't also put socket Intel LGA 1366 processor to Intel LGA 1155 motherboad. All AMD processors today use AM3 socket, but Intel has many different sockets: old LGA 775 (Intel Dual Core, Intel Core 2 Duo/Quad), LGA 1366 (Intel Core i7 900 series), LGA 1156 (Intel Core i7 800 series, Intel Core i5/i3) and the newest LGA 1155 (Intel Core i3/5/7 2000 series).

Choosing the processor for gaming is not easier than finding the right graphics card. If you are on tight budget then you don't necessarily need an expensive quad-core processor, only few games out there take advantage of processors with over 2 cores. Getting a fast dual-core Intel i3 or lower-end quad-core are both good choices. I suggest buying a gaming computer with good graphics and average processor, rather than very good CPU and bad graphics card.