hi, i only play seasonal hardcore and have been top 100 many seasons. i only say this to give some credibility to my recommendations

the best speed builds are probably the same as softcore, WW barb, TR monk, the new DH set

the truth is that any C-tier or above build will get you to speed T16s, the difference is mostly in higher GRs. Some builds are just very tough to go past 110-115. But any build tuned properly is probably fine to to T16s once youve got the handle on it

mage is a tanky class in general but its just kind of bad right now. necromancer isnt good for hardcore unless youre playing meta groups. its just not really a good solo pusher or speeder, and imo its just not that fun to play. the WD set from last season is still good too.

i prefer crusader so i mostly play crusader. im goign to play hammerdin this season, which isnt the fastest build for speed runs, but an optimized hammerdin will sill go GR 100 in 3-4 minutes. ill only consider swapping to the heavens fury build if i get capped out on GR progression

so the TLDR summary-- most of the same stuff in SC is good in HC, you probably are just building it slightly differently to have your cheatdeath on and not to greed damage too much like they do in Sc