I'm a bang for the buck guy, and while I think the terms "audiophile" and "$50" are mutually exclusive (former audiophile here), I do believe you can get some very good sounding headphones for $50-75.
I use the Ultimate Ears 350 series as a phone headset for calls, and they have very solid music performance for $60. These are "in-ear" headphones, which can be hit-or-miss on fit, and improperly fitting ear canal phones will not sound good. So, that's the caveat on in-ear phones. Here's a link to the UE 350 series without the microphone for cell use: http://www.bestbuy.com/site/Ultimate...&skuId=1258684
Avoid "earbuds" - very few will deliver what you are looking for. These typically do not form a seal, and can be uncomfortable if you do try to get them to seal. "ear canal" or "in ear" phones with silicone tips of various sizes will be the ones to look for. You have to spend time fiddling with the various tips and positioning to get the sound right.
More reliable performance will be found on the standard type headphones that clamp your head
For your price range, you will not likely find many circumaural (surround the ears, versus sitting on them) but it is worth seeking those out, opting for "closed" type based on your music preference. "Monitoring" or "studio" headphones would probably be your best bet.
Audio Technica makes good phones for the money. The ATH-M50
might fit the bill for you, despite the fact that they are a bit pricier than your $50 limit. The M30
's are a notch down, but seem to be a good value.
There are numerous headphones with smaller earcups that sit on your ears that also offer decent performance.
This site is the headphone equivalent of this here fine bicycle forum: http://www.head-fi.org/
they have extensive headphone reviews and active discussion. There is very likely a pile of threads on the sub $100 performers.
Beware of the current trend (your rap artist reference is a clue) towards headphones with exaggerated bass response, often at the expense of detail in the mid and highs.