Ok Denon make some decent cans, but I would only buy a few brands. Beryerdynamic makes greats cans but they can run a bit pricey. So with that in mind, I would recommend Sennheisers as the best all around quality can. However, for portability I would definitely recommend in-ear monitors. Shure makes, in my opinion, the best in ear monitors. I have the SE 315s but also have several of therir previous monitors. SE315 is $200 and I use mine with a DAC Fiio E7, which I got for 75. Put if using with ipad than you will also need the camera connection kit which runs $35.
The AKG quincy Jones 701 have great sound and some moderately good repsonse. The thing between cans and in-ear monitors, is that becaus emonitors are smaller they can produce better and clearer highs, as well as better overall frequency response. If you like electonic and hip hop than you need a can which can go from deep bass to high treble quickly without any muddying of the sound. In ears are better at this capability in the given price range. Obviously cans can outperfrom if they are connected to a $700 amplifier and lossless sounds sources, but for most people we have 320kbps and some apple Losless finles and maybe some flacs. For those people, the best you'll get is the Shures with a DAC. The Shure 425s are an upgrade on the 315 with a wider frequency response and slightly flatter/more natural EQ. Also the in-ear monitors have superior noise isolating. I use mine on the subway and trains everyday and can't hear a hting other than blissful music. Plus the in-ear monitors can be coiled up and stuffed in apocket easily. And the cable is replacable, which i had to replace once when i dropped my ipad and it bent the 3.5mm connector. So between the repsonse, price, dynamic EQ, noise isolation, portability, and overall sound quality the Shure SE 315 with E7 DAC is my recommended choice for you. If you must have Cans than go with closed back sennheisers. But with try to stay under 60 ohms other wise even the E7 wont be powerful enough to run them properly.