Yes, 70% of the sound is given by the headphones, but high-quality headphones, well amped, will reveal a crappy source... Or crappy tracks!!! Crap in, crap out.
Especially if you use a computer as source and not a CD player, and especially if you use high-res files, DACs are important.
Proper OS configuration and software for what concerns the computer, jitter reduction stages and sought-after analog output stages for what concerns the DAC are needed for a loyal playback.
By the way, nowadays "entry level" priced DAC give objectively very good results, since the technology implied in most DACs is extremely similar, at any price range.
If you don't need top-notch fully balanced impedance-matched rig, an entry level DAC with a couple of RCA outs could be a definitive choice... Just... OK, headphones make 70% of the system sound, but don't expect expensive headphones to sound faithfully out of your iPod, don't expect your headphone amplifier to make a difference when connected to the "green socket" of your PC, don't expect an expensive DAC to play any role if you are using an old supermarket PC running Windows Vista SP 2.0 out-of-the-box.
I'm not saying I can hear hard-disks (as some audiophiles claim, LOL), but if you're running Windows, hoping your computer is silent, you need to set it to prioritize the audio feed and bypass the really crappy default software mixer.
(To my ears, computer configuration and DAC's connection to it make more difference than the DAC itself, and from some amps to others... It's useless to run, convert, amp, whatever, a dirty or constantly interrupted signal!)
I'm not saying that there is any "better" OS to playback audio, but Windows needs a little configuration to get a good result. (actually it's about installing a couple of drivers)
The best of the best (but I'm not saying anybody needs it) is to feed the DAC through a internal sound card, to avoid all the USB flaws.
The best of the best of the best, to do it from another (small and cheap, though) dedicated computer.
And there are people around which are so picky on that you'd not imagine!
Could you give us some more details about the rest of your system, or about the rest of the budget?