Well, if we're recommending non-DC titles... Lazarus and East of West have the multiple characters/factions/houses "Game of Thrones" -like stories.
DC Vertigo/Wildstorm (mature readers):
How to Get Into Comic Books (13:40) | Patrick Willems
Consider your intent/commitment. Think about your favorite shows, movies, books, etc. Reading primarily for enjoyment or encyclopedic knowledge? Collecting? Have the time/resources to read 50 or 500 comics per character?
Don’t try to read everything at once. There’s too much. Forget about catching up, continuity, universes, etc. for now. Older comics can be an acquired taste for modern audiences, so they aren’t necessarily ideal starting points. Writers change often, characters get re-worked, and origins are re-told. Remember, there are many great characters, creators, publishers, etc. to explore.
Pick an interesting character/team and seek their most popular/acclaimed stories. Focus on self-contained, complete stories in one corner of the universe. There will be unexplained references/characters, just persevere or Wiki. Don’t let the tangled web of shared-universe comics overwhelm you. Think of it like solving a jigsaw puzzle one small piece at a time until you finally see the big picture.
Discover your preferences and let them guide you. Don’t get stuck preparing/over-analyzing, just start reading. Do you like/dislike old/new comics? Specific writers/genres? Cartoony/realistic art? Familiar/weird concepts? References/self-contained? All-ages/mature content? Follow these instincts. Didn’t understand a reference? Maybe read that next.
Or skip to the 2016 re-launch DC Universe: Rebirth event and then any Rebirth series #1.