I’m very happy with the Beyerdynamic DT 770. They aren’t the prettiest headphones you can find, but the sound is great, they are super comfortable and they are built to last. I have the 250 ohm version and my current laptop can power them without problems (but I’m using an external soundcard anyways), my phone and mp3 player both are a little quiet.
Since they are far below your budget of $330, you should also get a soundcard with headphone amplifier, if you don’t already have one, as you will notice the difference to cheap onboard cards (even more so if you spend all of the $330 on even better headphones) and the headphone amp will definitely power the 250 ohm (or possibly even higher impedance of more expensive headphones).
If you want more mobility, you can also get a version with 80 ohm. (There are also versions with 32 and 16 ohm, but generally, you’d want to go as high as possible and 80 ohm should be fine, even for phones, if you don’t plan to listen at extreme volumes.) In that case you’d still want a dedicated soundcard for your PC, even if you don’t need it for the volume.
I forgot to address sound cards in my first post. I agree with Frank. I suggest you take some of that budget and get yourself a decent external USB DAC/headphone amp. Massdrop carries a bunch of those as well. I have both my headphones and desktop monitors hooked up to a USB DAC/amp and it smokes the motherboard’s built-in audio.