Brightness on a headphone is a personal preference. Some call it detail and air. Many think the HD800 is fantastic, and not bright. Either way, they are on the brighter side of things. Fo what I listen to, I don't have much use for them except classical music. Though the imaging and soundstage for EDM is cool, just not enough bass for me.
It is my personal opinion that the HD800 won't be punchy like you want for j/kpop, and might be a little too revealing/cold for movies and games. Again, this is my personal preference. I think the Fostex TH900 will be a far more fun all-rounder for you. Problem is, you've blown most of your budget right there. But unlike the HD800, it doesn't need a great amp to shine. It'll sound great out of most anything. Power with a Fiio E9 for now and upgrade later if you want. It's my opinion the TH900 + Fiio will be more fun and relevant to you than HD800 + A1.