You would also need a new motherboard and new memory and likely a new PSU(I wouldn't trust the one you got with anything expensive) and a SSD to improve load times and make stream-watchers happy that they aren't staring at loading screens for very long, etc.
A new build will contain something like the following.
CPU ~ i7-4670k
CPU Cooler ~ Cooler Master Hyper 212 Evo
Motherboard ~ MSI Z87-G43 Gaming ATX or a ASRock Z87M Extreme4 mATX (depending on what case you get)
Memory ~ 2x4GB(2 sticks of 4GB) 1600mhz memory, g.skill, crucial, corsair, whatever it cheapest usually works.
SSD ~ Samsung 840 EVO 250GB
HDD ~ WD Caviar Blue 1/2TB or Seagate Barracuda 1/2TB
Power Supply ~ EVGA SuperNOVA 750W 80+ Bronze rated is generally fairly priced.
Case ~ Fractal Define R4, or you can just re-use your current case.
GPU ~ Geforce GTX 780/780ti Asus, MSI, Gigabyte, EVGA are all good ones to pick from and come with nicer coolers than the stock ones.
Disc Drive ~ Grab a cheap one, they usually run around 10-15
I'll snoop around and see if I can find a site that I can work with.
edit : Are you talking euros or dollars when you listed your budget? Pretty big difference there.
And
www.oc.nu seems to be a decent site to get parts off of if my google-fu is correct, though browsing it through google translate is a bit of a pain in the ass.
Probably best off waiting for someone else(someone from the UK/EU would be nice) to chip in here