It is all relative to what kind of sound you prefers as many great headphones may sound different. I own HD595 (and I don't think they really cost $339 anymore I paid around $250 3 years ago) and they are some what neutral with open sound stage as if you're sitting front row of a concert hall.
I am confident that you will be able to find something excellent under $500 but HD600 and above for sennheisers will require you to have amps to get most out of them.
If this is your first time getting into audiophile-quality headphones, you don't have to spend alot of money to notice the difference coming from lets say apple earphones...
some of the headphones I went through/heard good stuff about are: Sennheiser HD280 pro, Sony MDR-V6, Sennheiser HD595, Grado SR60(i), Shure SRH-440, DENON AH-D2000(sounds the best with proper amp/dac but is not necessary; perhaps you can start without one and get one later).
I'd recommend HD280 pro or HD595 to start off with.
Where could I get an amp, or is it included?