I'm not an expert but I'd say a relatively neutral sounding headphone with mabye a slight edge in the bass region would fit those genres best. Do you have a ~200€ recommendation that fits that signature for me? For the Amp/Soundcard I can go to the according sections.
The Shure SRH 840 should give you that with its mid bass hump. [That's based on US pricing.]
Can't help you with the computer questions, as I do almost all my serious music listening by way of CD's and vinyl.