I'd hesitate to recommend the 5830. Tests showed that while it performs between the 5770 and 5850, it's a bit closer to the 5770, which for about an $80 premium, is too much at current prices.

I wasn't really impressed with the benchmarks although it would be a solid buy at $200.

Alright, I've updated the first post now and I have every part accounted for. It would be great if you could let me know:
A) if everything is compatible.
B) if there is anything you would suggest adding/changing.

I also thought of something to save some money. I have 2 cousins living in California, so I could ask them to buy certain parts, which would end up cheaper (obviously, the little bit I save on a case would be lost in shipping costs for it). Will there be problems though, if certain parts are from the US and certain parts are not (power would be my major worry, or will the PSU take care of the voltage?).
Thanks again
GreyianStorm

Yes, I'd stick with the 5770 for what you want.

You could probably go a bit lower on the CPU if you're not doing anything too intensive. An Athlon II tri-core or quad-core would be 50-90 euros cheaper. Or if you value low power consumption/heat/noise, then maybe an i3 530, though it will be priced higher than its AMD performance equivalent.

Components from the US will be a lot cheaper (for example, your CPU and GPU would each be 50 euros cheaper ). But there will be shipping costs. Not sure about US/EU power compatibility for other components but anything without a direct connection to the PSU (CPU, RAM) should certainly work. The rest might work, but I don't know.

everything looks like it will work together. You may want to look into if the cpu comes with termal paste and if sata cables come with the dvd drive and the hard drive. you may also need a hdmi cable for the monitor.

ps. from the way your case is layed out you may want to buy straight to right angle head sata cables.

I was taking another look at the processors available on Komplett, and notice they have the Intel Core™ i5 Quad Processor i5-750 for an extra €15. Should I look at changing to that? If I do, will I have to get a different Mobo or anything?

Read the reviews on the LGA 1156 socket/P55 chipset motherboards used with the i5-750

http://www.tomshardware.com/reviews/lga-1156-motherboard,2463.html