If you're running straight out of your on-board sound card, then I'd personally get both a DAC and an amp (whether they're separate components or not is up to you). Doesn't need to be significant; I noticed a huge improvement comparing on-board to the AQ DragonFly v1.2 ($150, portable USB DAC/amp). Largest difference for me was bass extension and sound stage. The on-board soundcard just sounded congested, fake, and extensively digital / noisy in comparison.
Can't speak for more expensive amps though currently. Still trying to find an amp that would suit all the headphones I am looking forward to testing / buying.
I would definitely buy a DAC/amp if your computer / laptop is especially old (probably 3~4+ years). My cousin, for example, thought his Audioengine A5s were lacking bass (I thought they were hella bassy regardless, but I like my sound balanced) and therefore wanted a subwoofer to pair with them. He was running the speakers straight out of his probably 5+ year old laptop. Brought my DragonFly over and the difference was literally night and day (and I am not exaggerating. He was able to tell the difference and he doesn't care too much about the technicalities of audio / hifi. He just wants it to sound good). The bass basically just started hitting hard enough in his small room that he didn't see a need to splurge for a good sub and everything else was far more clear (though that is saying a lot for the A5s, personally). Before it probably rolled off around 120~180Hz (I don't know my frequencies exactly, but the lower mid-bass segment) whereas after it started hitting the high sub-bass frequencies as they're quite known to do.
Still only wish their frequency response was a bit closer to the HD650s. Still not a big fan of the treble, though I've grown accustomed to it.
