i have an ath-m50 (older model but same thing without removable cable)
a schiit magni would be wasted on them honestly as they do not benefit greatly from a good amp. also just adding an amp wouldnt bypass your audio issue. adding a dac as well would, but the schiit stack is $200. a fiio e10k is cheaper and would work but you're limited to stereo sound (no virtual surround) if you care.
benefits of an external setup (be it a soundcard like the creative omni or similar or an amp/dac like the e10k) would be no need to replace the jack on your case and good sound quality. the downside is no mic input, no virtual surround, limited features.
benefits of just buying a soundcard would be virtual surround, mic input, more features. if your pc case jack is broken you would need to replace it though (either get the replacement part to fix the case or use a front panel device with audio built in to connect to the soundcard).
either would work (soundcard or dac+amp). my suggestions would be the e10k, creative omni or xonar dg.
of course if you intend to buy some nice headphones down the line which would need a stronger amplifier (dt990, akg cans, hd650, etc) then perhaps buying the shiit stack up front isnt a bad investment just not as useful for the moment.
schiit products are certainly top notch, i just think its overkill for the m50. of course your money your decision and it would certainly work if you went that route.