Hey guys, thanks for the suggestions! In the end I went for:
CPU: Intel i5-7500 Kaby Lake
CPU cooler: None, went stock, not going to OC for a while.
Mobo: Asus Prime Z7270-P 1151 socket
Memory: Kingston Value DDR4 2400 MHz 8gb (thought I ordered 16GB but ohwell... it'll do for now)
Storage: Samsung PM961 SSD 256GB
VIdeo card: ASUS GeFOrce GTX 1060 6GB DUAL
PSU: Fractal Design Integra M 650 W
Case: Corsair Carbide Clear 400C Midi Tower
Edit: The price was about €1200, including OS
Finished building the thing a few minutes ago, first build ever, woo! It's up and running, but currently I'm making a Windows 10 USB to get an OS on it.
Only thing left to do is cable management, but after spending hours trying to make sure everything went in the right spot, and that everything was working just right, I just can not bring myself to start trying to figure cable management out...
Thanks again for the help, really excited for my first build