The 598's are practically the same headphone as the 555's. They won't be an upgrade to you. I bought mine because of that nostalgic reason actually. For example the HD598 share the same lack of bass, which makes them not that good for watching movies, and of course they can't really be used as portable headphones as they are 'open' (all external noises are heard). With the perspective I now have, it has to be said the 598's can't be considered to be neither 'mid-fi' nor 'hi-fi' headphones. For example the HD600's are considered to be in that mid-fi class and they destroy the 598's in every aspect that isn't soundstage, which in any case is grossly exaggerated in the 598's. If you are curious, I'm in this thread because I'll be again using the 598's, but that's because my Oppo PM-3's are reported to straight up cause hearing damage and I already have the 598's sitting at home. As for your questions, 1.- The by far best way to step up with headphones is to get better headphones. Sounds obvious, but there's many people that commit the mistake of getting DAC/amps to improve the sound of their 598's, when what they should have done is getting a better headphone instead. 2.- Amps start to matter once you get into better headphones, because those usually require more power to be driven. The 598's in particular improve a bit with an external amp, but not by much. On the other hand, the HD600 do sound much nicer with nice amplification. Personally I think it'd be a bit of a waste to use the HD600's with a Realtek soundcard, but I wouldn't mind using the HD598 with that. Also, DACs themselves matter less than the headphones and the amplification, but have to mention them because usually they come bundled with amps and in the end it's always a nice thing to have. 3.- The HD800's won't show their potential with your soundcard, at all. They are very picky when it comes to amplification, requiring way more power than the HD600's, plus that amplification has to be very clean. Also they vastly improve by performing a mod to them (the Anax mod), and so on and so forth. End game stuff gets complicated. I'd rather spend that 598+Amp money (which is the usual recommendation here) into getting better headphones instead, picking one in particular that doesn't require external amplification so that you could use them them with your soundcard extracting 80%-90% of how they could sound like with a nice DAC/Amp. My first recommendation is the recently released HE-400S from Hifiman, as I tried them the other day and they tick all the boxes, in sound, comfort and so on. They are considered to be on par with the HD600's, but without really requiring an external amp. The only thing to be aware of with them is that as a company Hifiman is known for its failure rates. For a second recommendation, you could get a high end headphone, plus a nice DAC and a nice Amp. I know it's much more expensive, but what usually happens here is that over the years people end up buying 10 cheap-ish headphones and 3 cheap-ish dac/amps, when financially the better decision would have been to get 1 very good one. And if you still want to get the 598's, as I did for gaming in mind, then it's not really necessary to get a DAC or an amp.