You opened up quite a lot of suggestions from people, which is why I said it was 'quite the question.'
Everyone has their low-down on the best way to go etc. and everyone here who has posted has great info.
For your question on where to find on line how-to on build your own, I'm not sure...I do remember seeing some things like that on Tom's Hardware. I do know that there is quite a lot of things to 'just know' about all the compents to put together, and for those that are 'into' computers, or have a natural desire it is fun and a productive learning experience. however, if learning about these compenents doesn't sound fun, then going with the name brand would be great.
I kind of equate it to cars...I'm not a gear-head and would not want to know the benefits of altenator A over Altenator B, or why a certain gear ratio is better etc. So I can't really recommend any specific brand components over another but here are some tips:
LCD screen - look for its bandwidth, contrast ratio and how well it deals with 'smearing' high motion video movement. they also have some problems with the angle at which you can look at the screen - just as in laptops where a 2nd person may not be able to make out the screen very well from a side angle. They are also fairly limited in maximum resolution. I currently have a SONY 17" w/ a max res of 1280x1024 and fairly good stats - but I also have a flat screen CRT as well.
(daveppeters covered this in his post too)
FLAT screen CRT - look for refresh rates, vertical refresh ... in a simplified explanantion ... determines 'how fast' the monitor is able to draw the information it receives. A kind of software work around this limitation is called vertical sync, which many games and or video settings in your OS will allow you to turn off - ie just let the monitor draw as fast as it can while not making sure to syncronize it with the coputer video output. However, 'tearing' and other anomolies will occur. "OMG he totally missed me with that shot!" is a quote that I'd may expect from someone with Vsync off - they missed the part of the motion which showed him getting hit. Also, look for vertical refresh rates of > 75 hz or so for whatever video resolution ie Vertical refresh rates will be specified based on which resolution like 60 hz at 1280x1024, 75 hz at 1024x768. So keep this in mind when you see 'MAX RES 1600x1200!' advertised because at 60hz it just sux. Under florescent lighting, which in itself flickers, low refesh rates on monitors can strain your eyes...especially on white background screens. I personally think anything over 75 hz looks pretty well. My Sony lcd is running 1280 x 1024 @ 75 hz.
CRT 'BOAT ANCHOR' BUBBLE FISH EYE Monitor. Okay so the title has a little bias.
These are the old type CRTs that weigh a ton, and aren't that bad...but after you use a FLAT screen CRT the difference is 'intuitively obvious to the most casual observer.' Not to say they are ****e in the least. I have used many old monitors (new at the time) and they peform quite well, and have/are cabable of great resolution and refresh rates and in now way are 'bad.'
Tomster was exactly right, imho, on the mouse. Many gamers like the optical mice and I have one - the extra buttons, mouse wheel scroll are extremely handy. Don't know if they still make keyboard like this, but watch out - some really cheap ones had a 3-key input limitation where you couldn't input more than three keys at one time...but these were usually the really really cheapo kind than shipped with 'brand x' clones. old PS/2 mice supposedly have better refresh than USB 2.0 mice, but I don't honestly think this has a major impact in gaming. Now the logitech wireless and other wireless have refresh rates less than wired mice. There are newr wireless mice, especially logitech's new one that recharges in a cradle which are very respectable. I have a wireless logitech key/mouse combo and I absolutely love it to death. My couch is now an extremely great place!
I think the $1000.00 quote on a previous quote is not an unreasonable budget for a kick-*** gaming machine at all. Some things, like video cards can run upwards of over $500 amercian, for a great video card - but you are paying a lot for something that only increases performance marginally. Kind of like paying an extra 3 thousand for a $10,000 car that has 30 more hp over the regular model...for the car enthusiast it is worth it.
Good look on your endeavor, and I'm sure that you will, in the end, come to have a love/hate relationship with your new computer.