Best bang for buck currently would be the AMD/ATI HD4870, excellent performance for a great price. I'd stay away from Nvidia because eventhough they have the fastest cards (I'm talking GTX280 and so on), they also are too expensive for the difference compared with say an HD4870.
Also, and this is true at least since Nvidia released their 8800 series, ATI drivers nowadays really are good. Usually the really new cards improve a lot with each new driver, but Nvidia takes a lot longer to iron out driver bugs lately.
When it comes to CPU, go for Intel Core 2 Duo or Intel Core 2 Quad. Anything from an E6600 and better is fine, don't go for the really really cheap Core 2 Duo ones though, you might end up buying an underclocked and slow processor.
I'd recommend 2Gb of at least DDR2 (800mhz) memory, but depending on the motherboard you go for (for example a X38 or X48), you might end up buying 1Gb DDR3 RAM first... It's a bit more expensive, but in the long run it's worth going for. Just upgrade to more DDR3 ram by the time you can afford another extra 1Gb.
All in all, if you want to buy a PC that will be able to run the latest games AND will be able to keep up for a year or two, you'll likely spend about 1500$ - 1000€ at least. In my opinion it's totally worth it though, even though at the moment graphics card and CPU development is going at insane speeds.
I'd recommend against 64bit Windows by the way, way not enough companies fully support 64bit.
As far as i know not many applications now are optimised for more than 2 cores.
Actually, that's something of a myth... there are lots of programs already capable of making use of the extra cores. Also, multi-cores really is the future, so why not make the switch now? More importantly, all future games will make use of quad cores... all PS3 and Xbox360 games that also end up on the PC are usually able to make use of multi-cores.
As for the HD3850, it's a good card as well, but you might want to check out the newer and faster HD4850 instead. It's a bit newer, a lot faster and the price really isn't that much more (about 30% usually, which translate to about 60€ or so).
Cheers