I really like my DT770s - mentioned earlier, but I have to say I don't really trust them for mixing. Fine for tracking and nice listening phones, but they don't expose things like you want (IMO). Not sure what your use cases are, other than having something more isolating. And, initially, your budget was $50 which is a long way from the DT770 range.
I think the Sonys (MDR-V6 or 7506) with upgraded pads are a nice option for listening and while I don't mix with them, I trust them pretty well for checking something I think is finished - it has to sound good on those. (They are closed back so can be used for tracking.) Still, not $50... (I have my old V6s by my notebook right now.) Of course, you don't *have* to upgrade the pads right away, but you'll be replacing them soon enough.