I'm new to Arduino and would like to know the following:
I'm looking for a way to power on (and off) a pc using a IR remote
Simeric PCS-2 has this already built board, but I'd like to build my own (and save some bucks 
)
I'd like to know which parts I need and a guess of the price
I live in Belgium so shipping fees are applicable too
Good idea. You'd need to hook your arduino up to the power switch jumper in your PC. I don't know how much power goes through those pins, but it's probably 5v or 12v so you might want to use a relay.
Have a look at this: http://www.fabiobiondi.com/blog/2009/11/control-your-arduino-using-an-infrared-remote-and-the-ik38khz-sensor/ - you'd want to put your relay where the LED is. You'll want it to press the switch for a short time rather than leaving it on.
The other idea (more complicated, but more fun :D) is using Ethernet Shield and Wake On LAN, if your motherboard supports it 
But that is rather hardcore solution...
Most boards will support WOL, but an arduino and ethernet shield is going to cost more than the device he mentions.
Unless he wanted to power on a whole cluster by pressing one button on an IR remote...