I've been buying Iron Fist comics and storing them in my comics filing cabnet under the Iron Fist name. It actually reads fairly well as a continuation of the Immortal Iron Fist. The only real errors are whether or not he's a billionaire working with Rand Enterprises or if he's broke and running a dojo for kids. That annoys me some but I can get over it.
In case anyone wants to continue the adventures of Danny Rand in a reading order that's best for Iron Fist fans I'll list it below. Danny's not always in every issue but it's there for a reason.
Immortal Weapons 1-5
Thunderbolts 137
Deadpool Team-Up 886
Shadowland: Power Man 1-4 (you can also add Shadowland proper since Danny's a decent roll there)
New Avengers (vol. 2) 1-6
I Am An Avengers 1 (Danny story)
Heroes for Hire 1-5
Power Man and Iron Fist 1-5
Iron Man 2.0 5-7 (note... this story has a big reveal about Danny that's never been followed up on regarding New Avengers 1-6, so it might be ignore worthy if nothing comes of it, but the story is good at least)