For those genres I'd recommend something other than the DT-770. They're really more suited towards hip-hop and some electronic music, though they do well with some of the more modern, heavier rock bands. It would help if you listed if you have any amplification, what you're going to be be playing music from, and what environments you're going to be listening under (i.e., does it matter if sound leaks out or noise leaks in?)
I haven't heard the HE-300, but I have heard the HE-400, and it is great with the genres you listed, so it's certainly worth looking into if they're at all comparable. Another option is to consider some of the Grados in the price range you're looking at. I don't know if the $250 list for the HE-300 is your price ceiling, but for $50 more, the SR-325i is excellent for those genres (rock would be its strong suit, with large-scale classical works being its weaker point). Mids and highs are the Grado's specialty. Its sound stage is not massive, but it's sufficient.
