So I haven't played since vanilla...is it worth going through the story mode any more or just jump straight into Adventure Mode?
The main game core story is really bad. Like really bad. 80s-Saturday-morning-cartoons bad. Maybe some of the optional dialog is ok? I took in the story only once, right when the game first launched. There's neat stuff to be explored in the Diablo universe, but they totally missed the mark imo.
I could be totally misremembering, but Diablo 2's story was more minimalist (probably due to games being smaller back then); it had more of a "tell, but don't show" sort of vibe where your mind would fill in the details & engage with the mystery of what wasn't there. One of the best lines that stuck with me was when you fight Diablo in 2 he growls, "Not even death can save you from me," as a sort of nod that when you die you wind up back in Hell and he's still after your ass. That's really effective writing, at least it was at the time. 3 is the polar opposite, "show everything and leave nothing up to the imagination". Like in Act 3 when the 'Genius Demon Tactician General Azmodan' literally tells you every step of his SECRET DIABOLICAL PLAN TO DESTROY YOU PUNY NEPHALEM. Ugh.
HOWEVER, everything else about the game is incredible! I've played it on and off since launch on PC, then 360, then PS4, and I'm considering it on Switch. It's a great game.
tl;dr For max fun, play the story to about level 15-20, then go to Adventure Mode. The game is about smashing screens of mobs, watching all the numbers go up, and that sweet sweet dopamine release when a legendary item hits the ground. The best and most fun way to do all that is Adventure Mode. Killing stuff in Adventure is really slow until that lvl 15-20 mark, so the story quest exp is the fastest way to get there.