dac = digital to analog converter. this is what converts from the digital signal a pc outputs to an analog format speakers need to power.
amp = amplifier. this greatly powers up the signal out of the dac so that it may push speakers. otherwise you would get hardly any response due to low level signal.
in short... with headphones you would need either a dac+amp, use your pc's onboard audio with an amp or get a soundcard (which is basically a dac+amp+software in one) because they are unpowered so need to have an amplifier to drive them. powered speakers can use just a dac only since they have their own power source and own amplifier built in (headphones do not).
best for $70?
fiio e10k is a good entry level dac+amp more than capable for the hd598. decent quality stereo sound.
the creative z or xonar dx are good soundcard options. they give you virtual surround as an option if you like that. the z has a better amp but the dx has a better dac. i'd likely go with the dx but its your choice
a user managed to get virtual surround working on an external dac+amp when their onboard audio soundcard supported virtual. how i can not say but it might be possible and i can confirm in at least some scenarios it is possible. otherwise, dac+amp solutions are 2.0 only.