Well first try to think off what the new PC would be used for. Most games and programmes do not need a top of the line CPU. Do not stare yourself blind at number of cores, clockspeed or cache, you need to look at benchmarks. Toms Hardware&CPU charts give a fairly nice overview. Look for instance for a game that you might be willing to play as soon as you get the new PC, look how good processors fare with this game. Look especially in the middle. Any CPU that does not slow down a chosen game regularly below 60fps is adequate. The number 60fps is what I would choose, you can choose whatever you want, for instance 30fps or 200fps, your choice.
Maybe you want a little headroom so pick one that might be a bit overpowered, but not too much since cost rises exponentionally. As a rule of thumb AMD is cheaper in mainstream, Intel has got High-end CPU's at high-end prices. But investigate, it's only a rule of thumb and it might differ from country to country.
When you have chosen a CPU, pick your mobo. Look at what features you want like #Sata ports, #IDE ports if any, #USB ports, has it got front panel audio connectors, onboard video, serial/parallel ports, Crossfire/SLI etc.
This might be the most intensive research since mobo's generally just do what they are meant to do. Go with a brand that you trust, pick a suitable mobo and read user reviews. Repeat till you found a mobo that you think you can rely on and has the features you need
Next RAM. 2GB would be the minimum, 4GB even better. Look at your mobo specifications, has it got 4 Ram slots, then ok, if not choose antoher one. This in the light of future upgrades. I'd recommend picking 2*2GB if you want 4GB and 2*1GB if you want 2GB. Timings do matter, but not so much as everyone would like to believe. CL5 is good, CL4 is better but generally much more expensive to justify in any way.
Brand does not really matter. There are so many brands, but most of them buy their ram chips at factorys, put it on a PCB thats also bought at another factory, assebled at another factory and put their own sticker on it. What you should look for is warranty, and how it is handled. Most brands give 10+ years so that should be ok. If its got heatspreaders, fine totally unimportant
Now video. Do the same as with the CPU. There are also Toms Hardware GPU charts. Again, do not exaggarate, there is no use in having 120FPS, if 60FPS will do. Look for some suitable video cards, look at the prices and pick one. Also pick a brand you trust and that suits your needs. If you want to run nVidia SLI you need a motherboard with nVidia chipset, and you need two in most aspects identical video cards. ATI CrossfireX works (I think) on all mobo's, and does not need two identical video cards.
But running dual video cards is mostly just a waist of time, money and your nerves so I wouldn't add this as a criterium. It often does not work, only works with workarounds, works half assed, or is mostly only a marketing argument so they can put a nice sticker on the box. By the time you want to place a 2nd card in your PC there probably will allready be a video card available thats just as fast as your SLI/Crossfire rig and more cost&power efficient.
Harddrives. Well 1st you want it to be reliable, 2nd reliable and last but not least reliable. Problem is you won't find any hard, real and objective data on it. From personal experience I can say in the past I have always chosen Seagte but from the 6 drives I bought in the last 7 years 4 are dead, and the fifth is on its way too Harddrive graveyard too. Oh and they brake down always after the warranty has passed
. All were used in cases with cooling in front of the hard drives, and my computers stay on for most of the day, so no constant power up/downs, still they die.
So now I went for Samsung (spinpoint T166, 500GB) but I cannot give data on reliability since I only have it a few months. But they are cheap, very silent (better than Seagate) when not reading/writing, and a bit faster. Still its not top of the line in regards to speed but adequately enough. Samsung now has Spinpoint F1 drives to replace the former drives. From benchmarks the F1 1000GB seems very fast, but he models with lower capacity do not since they use different platters.
CPU cooler, a very subjective topic, again read benchmarks. It should be quiet and provide good cooling. Personally, Zalman is overpriced and hyped, not silent at all even not at lowest speeds. For my new PC I bought a Scythe Mugen Infinity. It is unaudible and cools very good, but expensive. Though not as expensive as Zalmans coolers.
Power Supply, again very subjective topic but there are some things to look out for. First thing would be brand and price. Avoid brands like Sweex, Qtec etc. You will find they always give you high wattage at a low price. In comparison to other brands it sounds too good to be true, and in 99% of the cases it is. A power supply that has a stated power output of 450W should really deliver 450W even for hours on end and not go up in a ball of flames at 300W. Another rule of thumb, if it is heavy, it means they didn't cut on cooling blocks which are expensive. Another thing that is important but you can't really check are safety measures like overheating, overpowering, short circuiting and stability of the voltages under differing power loads.
Again some personal experience, in my younger days I did not have that much of a clue about PSU brands so mostly just went with whatever el cheapo PSU was fitted in the case. Result are several destroyed PC's.
Now when you have chosen all your parts, go back to the beginning of this post and build another system within your budget, do this a few times and put the systems next to each other. Look at what benefits and drawbacks of all setups are, and pick one. Then finetune it.