I have a couple of suggestions!
Books that are currently ongoing:
The Vision (2016): This is probably the best ongoing series being published right now. It is, so far, an incredibly well written and hard hitting book tackling some complex and dark themes. 10/10 and it's the one book I activley look forward to every month.
Moon Knight (2016): The new run of Moon Knight is incredibly thought provoking with a focus on Marc Specters insanity and how that ties in with the narrative and artwork. This book is a close second the Vision for best book out there right now with any competition for third place fairly far behind.
Old Man Logan: This is an ongoing series at the moment, but it all started in 2009 with Wolverine: Old Man Logan. It continued in 2015 for a short series and again in 2016 where it currently is. If you just want to read the most recent 2015-2016 runs, you will get it and they are some of the best Logan stories around.
The Walking Dead: Sure you can watch it on TV, but there is something about the comics that you just can't get on cable. And trust me, they will keep you on the edge of your seat. One of my favorite series ever (and this was before the show!)
Spider-man/Deadpool (2016): This book is gold. You can't put two characters that are more alike but so vasty different together and not get fireworks. And what glories works they are!
The Ultimates (2016): Yeah, I almost forgot about this book after I talked about Moon Knight, but there is just something special about this run of the Ultimates and the cosmic side of the marvel universe that's exceptional. Idk if its the art or the writing, but it's really got my interest.
Oldies but Goodies:
Uncanny X-Force (2010): I can't recomend comics to someone and not, straight off the bat, mention Uncanny X-Force. To this date it is one of the best series I have ever read, with a combination of great stories, an amazing roster list, and fantastic art. If you want to read a bit of the backlog and storylines leading up to this book, I can also recomend X-Force (2008-2010).
Batman (2011): Scott Snyder's run of the New 52 Batman was fantastic from start to finish. Sure you could look at older stories and shorts that are iconic (like Killing Joke, Dark Knight Returns, ect.), but if you want something more modern, this 52 issue series is worth the read. The End Game story arc is well worth the price of admission.
Batman Eternal / Batman & Robin Eternal: Yes, I do love batman. Both of these books dovetail into one another and are extensions out of the aformentioned Batman (2011). But holy cow are they worth the read. I really loved them, and if you are any kind of batman fan, these are must read stories.
Justice League (2011) Darkseid War - issues #40-52: The Darkseid War arc at the end of the Justice League's New 52 run was a great read. There are a few solo one-shots for each member that takes place in the middle of this run that detail the...changes...that happen and will be worth a read if you want to suppliment the main arc, but I wouldn't call them nessesary. I don't believe I read the whole run of this series, but I certainly read this arc and it was action packed awesome.