So here's a guide to comics to read if you're new to Iron Man. If you've seen the three Iron Man movies, you've honestly got a pretty good handle on his origin so you could skip right ahead to the newer stuff if you wanted too.
Invincible Iron Man Omnibus series
If you are one who wants to start at the very beginning, then this series is the way to go. It collects all of Iron Man's early appearances from Tales of Suspense to Avengers.
Iron Man Vol. 1: Demon in a Bottle
If you're interested in starting the Iron Man solo books, this is where to start. Tony didn't start getting his own adventures until the seventies or or so.
Iron Man: Iron Monger
This might be a story line of interest to fans of the movies. It has Stane (the villain from the first Iron Man film) and Rhodey starting his superhero career.
Iron Man: The Dragon Seed Saga
If you're interested in the Mandarin, the villain from Iron Man 3, then this is a good place to look. Just be warned...it's different from the movie and racist.
Iron Man Omnibus by Kurt Busiek and Sean Chen
Yes, there are two omnibus. The first series is the original by Stan Lee. The second is this one, that brought Iron Man into the early 2000s by Kurt Busiek and Sean Chen. If you're more interested in modern Iron Man, this is a good place to start.
Iron Man: Extremis
Another story arc that might be of interest to movie fans is the Extremis story line.
Civil War: Front Line
Iron Man was a big player in the Civil War story line. This focuses more on Tony and Captain America during this time.
Iron Man: Director of S.H.E.I.L.D
Story arc that takes place after the results of Civil War. This is basically where Tony in the MCU is now. So if you have seen all the movies and want to just jump into the comics without going backwards story line wise, this might be a good place to start.
Iron Man Vol. 1: The Five Nightmares by Matt Fraction
Another possible good place to start while waiting for more Iron Man in the MCU movies.
Iron Man Vol. 1: Believe
If you just want to jump straight into the more recent story lines, this is a good place to start.