Motherboard > Graphics > CPU > Hard Drives > Memory > PSU
Obviousy a gross simplification but a generic guide in order of priority as to component importance. The odd one for most folks is choosing a good motherboard - it dictates how well everythign else will play together so is top of the pile. Assuming you don't get an ultra budget CPU graphics would be the next in line.
Re Branding:
Intel vs AMD - comes down primarily to cost (AMD cheapaer than Intel) but also pure single core speed (Intel) vs multi-threading performance (AMD). Generally AMD make great server chips and Intel make great gaming chips as games are mostly limited by single thread performance. But if money is on your mind you get more bang per buck from AMD. AMD are waiting on their next product revision to hit in a couple of months time so Intel 2500/2600 products currently have a lead for gamers.
NVIDIA vs AMD - Too complicated to call unfortunately too many variances between different products to have an overrall opinion. Consider Driver support (NVIDIA tends to have better) vs Color processing and number of heads (ATI/AMD win this one) vs memory for texture processing and GPU units (depends entirely on the product). You get a lot more bang for your buck by buying a second gen product rather than the latest and greatest - I'd advise you to get the best thing available 6-12 months ago
Hope that helps - choose a really good motherboard - the rest can be easily replaced/upgrade/added to at some later date.
Be prepared for surprises on the costs of good cases, heatsinks and cabling if you build your own - quality does not come cheap and CPU coolers easily hit £60 on their own (10% of your budget).
The disadvantage to building your own is you'll end up spending 25-50% more for a rig than buying a pre-built. The advantage is that you'll end up with the best components and reliability. Pre-built tend to focus on a couple of key areas and the rest is done on a budged i.e. scrimping on quality (particularly the motherboard/drive controlers/case). Personally I'd always build my own for the satisfaction of knowing its as good as it can be. But its sometimes nice to have someone else already have done all the hard work for you so we won't judge you too much if you don't
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500-600 budget:
CPU: i5-2500 (sandy bridge) only purchase motherboards released after 1st March as there was an issue with an earlier revision and SSD controllers.
Motherboard - SATA3, USB3 and a well known brand i.e. MSI/Gigabyte/Asus/AsRock and bear in mind the sandy bridge SATA issue so get a newly released board/revision.
RAM - get quality over quantity as you can always get more later. 2GB minimum DIMM's i.e. 2 x 2GB. Go for Crucial/Corsair/Kingston sticks - don't get no-brand or budget RAM! Go for tight memory timings over higher frequency unless you plan on overclocking your system.
Graphics: Make sure it has 1GB of RAM minimum and get the best you can afford.
Its easy to spend 150 on a case, 50 on a heatsink, 25 on cables and 100 on a PSU (325) so budget carefully on what you actually need. BUT - if you buy quality now then you'll have quality to re-use in your future systems!