Trying to figure out where to start with John Constantine is a mess, but a fun one. He's bounced between so many titles, it's dizzying. If you want the purest dose of the original scouse bastard, you absolutely have to begin with the original 'Hellblazer' run, starting with Jamie Delano's issues. That's where the character's voice and soul were forged—all the cynicism, the magic that's more about trickery and consequence than fireballs, and the crushing moral debt. Everything after, good or bad, builds from that foundation.
From there, it gets thorny. The 300-issue 'Hellblazer' series is the core spine, but it changes writers every couple of years. You can mostly read it in order from #1 to #300, but be warned: after the initial Delano run, Garth Ennis comes in and takes the book to iconic status with stories like 'Dangerous Habits'. Some fans swear that's the peak. Later runs by Mike Carey and Peter Milligan have their fierce defenders too, especially Carey's complex family saga.
Now, the modern stuff gets confusing because DC integrated him into their main universe. If you jump into the newer 'Constantine' or 'Justice League Dark' books without the 'Hellblazer' background, he feels like a different guy—more of a superhero occultist. My advice? Read the original 'Hellblazer' as far as you enjoy, then treat the New 52 and later stuff as a separate, alternate continuity. It's cleaner that way, even if it means ignoring some official numbering.