You've probably read a lot of comics in your time, but it's unlikely you've ever read anything quite like the original run of Suicide Squad. While there was a golden age Suicide Squad, it was 1987 when a guy named John Ostrander started writing the modern age Suicide Squad, a bunch of c-list supervillians who'd been given a chance to cut most of their prison sentences down to almost nothing. The only catch? The missions had a fatality rate like you wouldn't believe, they were blacker-than-black ops and if you got caught, you were dead. If you tried to run, you were dead. If you failed at the mission, well, you get the idea. How did they enforce this? Each member of the squad was fit with an explosive fitted to you that would blow your arm off, and probably kill you. Sounds intense, right? Well, how's this for intense - this was a comic that wasn't afraid to kill off main characters. Regularly. Brutally. This was a comic where it wasn't a good idea to grow attached to anyone.
How do you get started with something like this? Well, you start with the person who built the Suicide Squad, Amanda Waller, nicknamed "The Wall." If there are three people with no powers at all in the DC Comics universe you don't want to mess with, they are, in order, Batman, Lex Luthor and Amanda Waller. Waller created Taskforce X (the actual name for the Suicide Squad) as a way to have high-powered disposable agents who could go and get things done for the government. They're the classic "nothing-to-lose" archetypes that date back thousands of years in storytelling. The Wall takes no prisoners, tolerates no excuses and offers no mercy. She is as dangerous a foe as possible.
The Squad has a few members who are, generally, part of the regular rotation, and I don't think I'm spoiling much by saying you'll see a lot of these three over the course of the first volume, including one of the people I'd want in MY rogue's gallery. That would be Deadshot.
Deadshot has appeared in a lot of DC stuff, and is a recurring villain in the TV show "Arrow," which draws from the Green Arrow mythos. His first appearance there was a bit lackluster, but we've seen him a couple of times since then, and the most recent appearance gives me a lot of hope that they're getting the hang of the character. The first time around, he's just too... well, uncool, for a lack of a better word. The character is almost psychotic, rather than the sort of detached, professional he's usually portrayed as in the comics. The most recent time we saw him, though, the character was much closer to the canon depiction, and that got me excited, especially since he's not the only one we've seen from the Squad on the show.
Ostrander's run of Suicide Squad dealt with politics, assassination, terrorism and a lot of the other real world nastiness that was going on at the time, and you would occasionally see people like Ronald Reagan and Mikhail Gorbachev appearing in its pages. Ostrander wanted to create a heavy mix of The Dirty Dozen, Mission: Impossible and just a hint of The Magnificent Seven, and I remember picking up the first issue in a Walgreens (back when comics were on spinner racks!) and thinking to myself, "This is a dark story!" I was 12.
I wanted to recommend "Suicide Squad" because I revisited it a few years ago, and was reminded just how daring the storytelling of the book was. Comic books usually build readerships based on getting to see the same characters every month, but Suicide Squad was different. Cliffhangers were genuine cliffhangers, because there were no guarantees for anyone in the Squad, and a character that saw years of plot development could be gone in an instant. I've always admired that. The whole first run's available through Comixology, and if you just want a taster, you can probably track down the first arc of the 1987 run in a trade paperback called "Suicide Squad: Trial By Fire" from a local comic shop, or from a used retailer on Amazon.
I wish I could tell you the new Suicide Squad was great, but sadly, it's only been okay at its best. Harley Quinn is absolutely the wrong character for this book, because there is zero fear of her getting killed off, and she's, in my mind, too unpredictable for Amanda Waller to have ever considered putting her on an already volatile mix. It feels too much like "well, people like HQ, so let's put her in a monthly!" and not a "who would make Suicide Squad better?" I see what Adam Glass (the first writer for vol. 4) was trying to do, and there are parts of it that work. He mostly gets Deadshot right, King Shark is an interesting addition, and the threat feels real. We even see some characters getting offed, which is good, but around the time Harley comes in, it all sort of falls apart. They've changed writers a couple of times since then, and I stopped picking the book up a while back, so maybe the new writers are helping, but I have to be honest - not a lot of the New 52 is working for me. The art's good, but I feel like they've abandoned sharp writing, and that hurts. I'll still pick up the trades for the new volumes, out of a sense of loyalty to the Suicide Squad concept, but I gotta be honest - my heart's not really in it, because it's just not working. I wish like hell it was, but it just hasn't sung in a while.
That said, you should still absolutely read the first volume. Just don't get attached to characters... the body count will keep on piling up.