The Extremis armor was an armor Tony could control by thought, and it seems to be summoned by instinct, as seen in Five Nightmares. In Invincible Iron-Man #25, Tony notes that running the armor was as natural as breathing:
The extremis armor wasn't stored inside Tony's body.
However, I do believe that the armor you're referring to is the Bleeding-Edge armor, which is, believe it or not, stored within Tony's bones:
I'm also a new Iron Man reader and in my opinion the best way to get into the character is to read Extremis, followed by Matt Fraction's incredible run (http://en.wikipedia.org/wiki/The_Invincible_Iron_Man). You should also read Secret Invasion before reading World's Most Wanted, and Fear Itself alongside, well, Fear Itself. I haven't read any of the Marvel NOW stuff, but from what I've heard it's mediocre at best. Iron Man by Joe Quesada seems great, too, though I haven't read it yet.
I already have a "The Night Gwen Stacy Died" in TPB format, and read Kraven's Last Hunt (though I am planning on getting a personal copy... eventually). I haven't read Back in Black, mind telling me what it's about? I remember reading somewhere that this story arc takes place after Pete's unmasking during Civil War, and during the story Peter goes all out in a battle against Kingpin, could be wrong though. Is it any good?