As the others have said, you can follow the Death of the Family just by reading the books your normally get. The likes of Batgirl, Suicide Squad, etc tie into the main story, but they usually don't have a direct impact on it.
Throne of Atlantis will be different, because that's an actual crossover. Part 1 is in Justice League, then continuing in Aquaman, then back to JL, and so on. So the 5 issues (JL #15 - 17 and Aquaman #15 & 16) will be one full story. You probably would get by without getting the Aquaman issues (I'm assuming from your post you're already getting JL), but it might be a bit like watching a 5-act TV programme or play and skipping Acts 2 and 4.
Hope that helps!