AMD VS Intel:
Today there really isn't much of a difference between these two brands. Intel's latest processers are a little bit faster then those of AMDS, but we have yet to see AMDS response to chips such as the core I7. Intel is a little bit faster at releasing newer models and drivers to their processors and motherboards, but aside from that the performances are almost identical. Though AMD can still do just about anything that Intel's processors can, generally with a slightly cheaper price tag.
AMD vs Nvidia:
Much like comparing the processers of AMD to Intel, there is little difference between graphics cards. Nvidia seems to have larger support from gaming manufactures and they tend to be a bit quicker when releasing and updating drivers to support the latest software. That is not to say however that AMD's graphic cards can not perform. They do very well and are generally a little bit cheaper.
A good website to check out is Cpubenchmark. They are a independant company that tests processers and video cards for all aspects of computing. They list those results in several easy to read bar charts.
When deciding it is important to do research on the different models and designs, then find the products that best match what you intend to do with the computer.
Online shopping vs Brick and Morter
Deciding where to purchase everything can be complicated at times, there are so many great places to go. So how do you decide.
Do some shopping around, when shopping online I like going to either New Egg or Tiger Direct. They generally have good deals for the products they sell.
For more traditional brick and mortar store you can check out a local Best Buy or if you have a store near that specializes in computers that would likely be a better choice.