Originally Posted by MalVeauX
The 250ohm DT880 would be my primary suggestion; it's universally easy to pair with any amplifier basically (both solid state & tube; both desktop & portable).
I don't think the HE500 would be what you want; it's a very natural headphone, not overly bassy, and based on what you're listening to, I would expect less than super high quality recordings, so it wouldn't make much sense to go high-end for it, plus the amplification requirements. I would suggest the HE-400 instead. And get an amp with it right away, like the Schiit Modi/Magni.
Agreed about the HE-500 not being what you want. While being great with all genres IMO, it is still much more amp picky than the HE-400 or the DT880. If you're looking for a more bass-filled 'fun' presentation over the DT880, and would prefer not to spend as much as the HE-400, I would recommend the DT990 250 ohm, which is also very easy to pair amps with.
The HD650 is not going to be as great as the other recommended headphones, because of its unnaturally smooth sound. Personally, I enjoy a more forward, fun pair of headphones when listening to the genres you listed above... not a laid back, 'forget there is music playing because it's so relaxing' type of headphone like the HD650.
All in all, I think, based on your sound prefs, all three of those headphones: HE-400, DT880, and DT990 would be great choices. I haven't heard the Mad dogs so that I cannot comment on.