I'm going to be completely honest with you, and it's something that surprised me personally. Of course, this is my own opinion so take it with a grain of salt, but when everything was working correctly, on the Gen 1 and Gen 2, amping did not make them sound appreciably better. The Gen 1s definitely need some amping for volume reasons, but it won't improve any frequencies aside from what higher volume can provide. On the Gen 2 I had the same experience, and on those, amping is completely unnecessary.
You could probably do just fine using a AQ Dragonfly Red, Oppo Ha-2, or Cayin C5 as a portable and at home amp. They will all supply more than enough for high volume listening with the Gen 1s regardless of source. I got the Dragonfly Red for my Gen 2s. I wanted to test if a Dac would improve the sound from my iPhone 6, but it really doesn't make a difference. It's just louder.
Take this info as you will, I also don't think expensive cables make much of a difference in sound quality either, and in my testing, that is what I confirmed, to my ears and a few others who tested with me at least. I can't wholesomely recommend the O2 for your Gen 1s, because it's bulky (if you plan to use it as a portable amp), and I did not have a consistent experience with it when testing them together. I think you'd be better off getting a portable amp, as those will provide much more than enough power, and if they are only for your H6s or other low impedance headphones, will work just fine for an at-home/listening station use too.
