Iron Man was first introduced in the 1963 Tales of Suspense #39. His most notable role in the comics was as a founding member of the Avengers, but Tony was far from a leading role in the comics until the success of the 2008 film kicked off the Marvel Cinematic Universe. For new readers, I would recommend Iron Man by Bendis (2015) as a very modern, complete, and really captivating story.
There are two series of paperbacks where Marvel is collecting older issues: The older 'Masterworks' series, and the newer 'Epic Collection' series. If you can find them, Epic Collections are way better value. Unfortunately, they don't look like they are reliably in print yet.
Marvel Masterworks: The Invincible Iron Man books 1-3, collecting Tales of Suspense #39-85:
If you're looking for books that heavily inspired the Iron Man films, you will find them in the modern classics Extremis by Warren Ellis and Invincible Iron Man by Matt Fraction. Both are great places to start reading.
The first book is Iron Man: Extremis, and all of Matt Fraction's Invincible Iron Man collected in two hardcovers:
The most recent complete storyline begins with Tony Stark in Invincible Iron Man (2015) but grows to be so much more. Bendis really built a universe of characters and stories all around Tony Stark which feel like a comic universe all to themselves. There are two main threads to this story, the main storyline, and a complimentary second storyline.
Invincible & Ironheart - Invincible Iron Man is the beginning of a brand new main storyline for Tony Stark and a great place for new readers to join his story. The storyline continues with Ironheart, featuring Riri Williams, a 15-year-old black woman and engineering student from Chicago. Stark is very much a presence in every single issue, but Riri establishes herself as a beloved character isn't going anywhere.
International & Infamous - International Iron Man was published alongside Invincible and deals with Tony trying to learn more about his past. The story continues under Infamous Iron Man, published alongside Ironheart, featuring Doctor Doom looking to keep the Iron Man legacy alive. These are less Iron-Man-y books. The art is like painting, and the storyline is mystery, intrigue, and resurfacing past pains, very reminiscent of Bendis' work on Jessica Jones.
You can read International & Infamous alongside Invincible & Ironheart as listed below, or you can skip them completely.
Iron Man by Bendis in paperback reading order:
A new writer and a new starting point for new readers has just begun. Only one paperback has been published, so I don't have much I can say yet, but so far the series has a strong supporting cast and tackles ideas like AI and virtual reality in ways that are really cool. I'm excited to continue reading.