Moved to HC forums.
Highest DPS right now are necro and wizard (necro highest GR for pushing, wizard highest for speed GR farming). Both are very squishy though. I personally went for wizard - died once, but it was my own mistake (as it is always on HC ;-)). Learned my lesson, everything good now. It's definitely a bit more challenging. Before that I ran a crusader on non-season, but deleted it - it's just too boring. Actually pretty decent DPS and super easy GR70 but never even in danger of dying. Doesn't feel HC-like.
Many people play the DH, because it offers the best trade-off between good DPS with relatively low chance of dying. I see a lot of people playing the Impale DH for that reason. But again, if I play HC and I'm not in danger of dying I might as well just play SC, right? So that sounds boring as well.
Basically: if you're looking for a safe farming class with a little bit less danger of dying and good DPS, pick the DH. If you want to be super safe pick crusader (but doesn't sound like that's what you're looking for). If you want to be a bit more adventurous and try something new pick the necro. And if you're absolutely mad and fearless and want the fastest mid-GR farming speed, pick wizard. (But be prepared to die! :D)
Edit: Just as an advice, have backup gear ready - and that should also already be re-rolled to the right stats and with backup gems, if possible. It really sucks if you die and have no backup gear, or that backup gear has to be re-rolled but you have no Death's Breath left. It's just nicer if your backup gear works right off the bat on T10. Basically I have 2 free deaths right now already because of 2 backup sets ;-)