I'm not up on these things, but I'll ask some questions that might help others help you.
By ear-cup, do you mean around the ear or on top of the ear?
What kind of music do you listen to? Are you most interested in bass (hip hop, pop, electronica, etc), midrange (alt. indie, jazz, americana, etc), or overall balance (classical, eclectic taste, etc)?
Do you care about isolation (blocking out external noise)?
Would you be willing to consider a portable amp plus headphones, if it stays in your budget?
Is headphone size important? (You have a small player, maybe you want small cans.)
What kind of experience do you have with hifi? Might be blasphemy to say it, but you might not need to spend $300 to get what you're after.
Oh, and don't expect a straightforward answer; you'll mostly just get folks recommending what they like, and you can read about those cans elsewhere on the forums.
Welcome to HeadFi!