While Nav is right, Invincible Iron Man is still pretty recent only on about issue 27 right now so you can find the trades pretty easily, the comic was specifically designed for the people who want to get into Iron Man after the movie. If you go to the comic store you can most likely find a copy of the Five Nightmares trade.
I'd say you don't even need to bother finding all the trades. I jumped on to Invincible Iron Man at the start of the "Stark Reassembled" arc (about issue 15 I think? Had those really striking covers by Salvatore Larocca) and haven't had any problems with the series. Might even be able to find the single issues if you look around for them!