Huge Iron Man fan here.
For early Iron Man stuff, you can’t really do better than…
Essential Iron Man vol. 1
Essential Iron Man vol. 2
Essential Iron Man vol. 3
That’ll take you from Iron Man’s first appearance through the late 60’s. First appearances of most of Tony’s important supporting cast, as well as the Mandarin, Titanium Man, Crimson Dynamo, Spymaster, etc… Some fantastic artwork from Jack Kirby and Gene Colan. Not every story is a winner, but they’re all worth looking at for the price.
Aside from Stan & Jack, Iron Man’s most revered creative team is David Michelinie and Bob Layton. As others have noted, some of their best work is collected in a couple of new Marvel hardcovers:
Demon in a Bottle
Doomquest
Demon in a Bottle is more or less the definitive Iron Man storyline, and what will almost certainly be the basis of an upcoming Iron Man movie.
Doomquest is a collection of Iron Man vs. Dr. Doom stories. It’s actually the first two parts in a trilogy of stories that’s being completed right now; the third issue of the latest miniseries just came out on Wednesday.
The Iron Man movie was roughly based on Michelinie and Layons Armor Wars, which is another of the great Iron Man stories. Highly recommended.
As other posters have mentioned, Extremis is the starting point for the modern Iron Man series. From there, the trade paperbacks are easily numbered if you want to keep up with them.
I’m going to highly recommend a couple of modern Iron Man miniseries written by Joe Casey:
The Inevitable features gorgeous art by Frazier Irving, and a very smart, compelling story that revamps a few Iron Man adverseries. I think it’s the best Iron Man story in years, and can’t recommend it highly enough.
Enter the Mandarin is a retelling of Iron Man’s first meeting with his arch-enemy, the Mandarin. It has a cartoonier style than The Inevitable, and it’s not quite as good, but it’s still one of the best Iron Man stories in quite a while, and does a really nice job of highlighting just why the Mandarin is the perfect foe for Tony Stark.
Now, if you really wanted to go all-out, you could get The Complete Iron Man on DVD. Unfortunately, these DVDs were discontinued once Marvel began their online database of comics, and prices appear to have skyrocketed since the last time I looked.
Too bad, because the DVD is a great way to get some really nice Shellhead material that remains woefully unreprinted, like Kurt Busiek’s Heroes Return issues.