I have to agree with Titi. If a custom built PC is more expensive than a prebuilt one, you're doing something seriously wrong. The only limitation to custom building should be your own skill (I wouldn't expect a first time builder to put together a rig with two graphics cards in SLI with water cooling, for example), but a fairly "normal" computer (air cooled, no hard drives in RAID, single graphics card, etc) should be no more difficult than LEGOs with a good tutorial on building a computer (Newegg TV on Youtube, specifically).
Of course, I can't recommend an AMD CPU for anything but the cheapest builds. Intel is almost always better than AMD in pretty much every other case. Graphics wise, Nvidea and AMD are usually very close, although Nvidea normally releases new cards first, with AMD not releasing their card until they have something that can beat its Nvidea rival.
On your build, though, Titi, you could save a buck by cutting the Hard drive size down to something more reasonable (500 GB - 1TB), since I can't fathom spending more on a Hard drive than on either the graphics card or CPU (seriously, the CPU and graphics in my current build come to over $500, while the hard drive is a mere $90 1 TB drive -- with 660 GB free). Hard drive space is also easy to expand, as you could use RAID 0 to "combine" drives, while you can only combine graphics cards of the same kind (and seriously, multiple graphics cards is a mess, heatwise and spacewise). CPU fan? If we're not overclocking (as would be expected for someone only spending 300-and-something on a computer), the stock cooler should be more than enough. For memory, if we're going for a budget build, 4GB is plenty and won't cost more than $30.
Personally, I'd say something more along the lines of...
CPU: Intel Celeron C530 @ 2.4 GHz = $45
GPU: Gigabyte Radeon HD 7750 = $110
MB: Gigabyte GA-H61M = $54
Memory: 4GB of whatever brand = $25
HD: Quick Newegg search found several 500 GB drives at $70 from reputable brands (just make sure it's 7200 RPM)
Optical drive: That sleek Asus one that literally everyone buys = $20
Case: We're going cheap, grab one with a built in PSU, like the Rosewill R218 @ 450W = $50
That's a total of $374 or 304 euros at current exchange rates. However, the Sandy Bridge processor offers a much better architecture over AMD, it's not all about clock speeds (although a $210 Ivy bridge i5 would do much, much better), and gaming wise, the graphics would be a major increase (seriously, the GTX 200 series is ancient). Of course, that'd also be another nice thing to upgrade: swap it for an MSI Nvidea GTX-560 Ti for about $270. Expensive, but the performance jump would be massive. A 200 series won't be able to play modern games at anything over the lowest settings. But for a budget build, the Radeon HD 7750 is a great buy, especially factory overclocked models (seriously, don't bother with stock cards, ever). The 7750 has 1 GB of memory and supports Direct X 11. I'd use the same DVD burner in a budget build as a high end rig: Asus's is fantastic, and Blu-ray isn't really much of an advantage in computers, at the moment. Springing an additional $20 could net a 1 TB HDD, and I'd recommend that, although it's not too hard to expand hard drive space by setting up RAID 0 to combine the drives in the future (although a third drive to use RAID 5 would allow a more secure setup, as your data would be backed up in the case of one of those drives failing).
There's no reason to buy 8 GB or RAM on a budget build. 4 GB is plenty, although going under is a bad idea (although RAM is cheap). The stock fan is fine if not overclocking, although the $30 Coolermaster 212+ is the king of CPU coolers for over clocking. Since we're going to assume that we're building a gaming rig, the graphics card is a lot more important than the CPU, as most games are fairly easy on the CPU. An SSD is hardly something to put into a budget build, but current prices are around a buck a gigabyte, and even a 128 GB SSD would give your system some serious clout, especially on startup and loading times. The read and write of an SSD can be ten times that of a mechanical drive, and they're more durable (no moving parts).
Of course, if we're doing gaming, you'll also need Windows, which will run you back an extra $100 (the Home Premium will do; the professional version is only necessary if using more than 32 GB of RAM, and the Ultimate version is just a rip off). Still, $370 ($470 with the OS) for a computer capable of gaming? Last time I saw pre-built computers at Best Buy, you'd need to spend at least $600-700 for that kind of capabilities, and even then there's the lack of choice in your components.
