Never do Bounties for gear, those are for materials. I suggest you do Greater Rifts on a comfortable difficulty, and then do Nephalem Rifts in-between if you need GR keys. Fastest way is to join one of the loot share communities though and ask for a loot carry.
Your skills are never at their full potentional without the proper gear, so you just need to figure out which build you wanna do and check what gear is the best. I suggest you aim for one of the meta bulds.
https://www.icy-veins.com/d3/necromancer-builds
You can try this fresh level 70 skill build while gearing up too.
https://www.icy-veins.com/d3/necromancer-leveling-and-fresh-70-guide-patch-2-6-season-11
I found the Necro to do very little damage without decent gear so you might get a bit bored. But personally I would suggest you ask someone in one of the communities (try to search for "necro" or "loot" etc) to make it a lot faster.
tl;dr the best way to get set items and gear in general is from GR and sometimes Nephalem Rifts. Fastest way is to get carried by someone higher up so you can get better drops.