This is my problem, I'm so casual on this I have no idea what great/god-rolls I should be targeting to make play easier.
If you have not picked up the quest for the recluse from shaxx in the past 2 seasons, I dont think its even available anymore. As to best weapons for PvE? Just general PvE? Use whatever you feel is the best. Its only the pinnacle activities like the raid and the 980 nighfalls that you need to coordinate weapons with your teammates. The rest of general PvE shit just use whatever you find to be the best stuff and the stuff you like the most.
But basically anything that improves range on any gun is the bst perk. Since range affects a whole bunch of hidden stats on any gun archetype. The other weapon perks to look out for is kill clip, rampage, which basically increase the damage of the weapon, and outlaw, which reloads the weapon quickly, thus increasing your dps because you reload quicker. So any roll with outlaw, kill clip, or outlaw rampage are considered god rolls. there are other perks they recently introduced too which increase damage too like swashbuckler to watch out for.
Also different perks are more important whether you play PvE or PvP. For instance kill clip is better for PvP, where you will probably score a kill, relload, then you have some time of added dmg for your next attack. In PVE rampage is better because when youre killing trash you constantly have a 3x stack of rampage going on the weapon, something that's hard to do in PvP.
Things like shot guns in PVP you want things that increase its range, quick draw and snapshots are god rolls since it allows you to switch weapons and ADS quicker. Opening shot is top tier and also look out for full choke for the barrel which helps with the pellets be tighter at range, full bore is top tier.
Same with snipers, snapshot quick draw is god roll. Since snies are usually one shot kills anyway, you want to be able to switch and ADS as quick as possible.