The number one time/way to get exotics and classifieds are during Global Events. After that, in my 4k+ hours, I have found LZ boss runs to be next. Anyone can do them. Doesn't matter if solo or in a group, and about any build can take them on. It is one named elite surrounded by 4-8 normal enemies. There's plenty of LZ boss maps online if you don't know where they are.