Well, the HF-2 is from all reports a spectacular set-o-cans, but hard to come by and pricey.
I tend to like to listen to open cans for the most part and my HD580's will likely be with me till my rocking chair days. Recently I've also been enjoying my Denon D7000's which I performed a portion of the Markl mod (do a search on it, interesting reading) on and upgraded with JMoney lambskin pads. They are quite breathtaking imho.
So having said that, I recommend looking onto the Denon D2000. It's a great all-around performer that is easily driven. Like all the Denon DXXXX cans, the bass is very prominent and somewhat uncontrolled. They are definitely fun to listen to in stock form. I grew tired of the dominating bass response and decided to mod my Denons. The results were very dramatic, and for the better. The bass tightened enormously and brought everything into better balance. I didn't do the full mod as I wanted to keep added weight of the mod to a minimum, and after all, I can always do the rest later if I want.
Honestly I recognized very little of the artists you display on you linked page
but if you like stringed instrument and acoustic/vocal stuff, open would probably be a better choice. Grado are some of the most easily driven open cans you can get, but many have comfort issues with them for longer listening sessions and they are pricier in the UK (so buying used may be the best bet on them). Many report that the Alessandro Music Series are a more balanced presentation than the Grado's, with a less in-your-face sound and less listening fatigue. At about $110 US you can get the Alessandro MS1i, which by all reports is one of the finest cans available in this price class (and higher). Then later if you want you can add a good external DAC/Amp like the Pico, Compass or HiFiMAN EF2, depending on how much you want to spend.