I am not trying to be difficult here but the questions really don't make a lot of sense to me. For example, please define what you mean by "history" of the blade? Are you talking provenance? The history of the period when it was made? How the smiths and schools were seen by history? Given that one sword is attributed to a smith who was the son of one of the most important sword makers in Japan, and the other is broadly attributed to a school, is that the kind of historical touchstone you are referring to?
These decisions for many collectors are normally based on their own interests and collections. If you collect Nanbokucho Soshu, then the Sa blade fits. If you collect Kamakura Bizen then Ichimonji would be the way to go. Other collectors just buy what moves them. Some just buy Juyo. Some want blades w/cutting tests or battle damage. Some want swords from particular time periods or schools.
Now, broadly speaking Iwato Ichimonji is viewed as the least prestigious of the four Ichimonji traditions, the others being Ko-Ichimonji, Fukuoka Ichimonji and Yoshioka Ichimonji. Hard core Ichimonji fans love the first two. But it ultimately depends on the sword, because even the worse Ichimonji can be great. That said I have seen MANY ho-hum Ichimonji. In fact, I was kind of unimpressed with the hype surrounding Ichimonji swords until seeing Paul Davidson's Yoshioka Ichimonji two years ago at Sothebys. It was like a revelation, like seeing a sword for the first time: a brilliant habuchi with choji that looked almost three dimensional; layers of floating utusuri like the clouds a plane passes through on its way to a landing. Never handled one like that before. I've seen some nice ones but this was the first and only one I ever handled where I remember thinking: "So this is what all the Ichimonji excitement is about."
So, If my pocket were full of change, and if I were hunting for an Ichimonji blade, I would want something at least which approaches that. But that's aesthetics, not history.
Elias, while I appreciate your desire to touch history, my recommendation is almost like a mantra or broken record on this board: keep your money in your pocket. Study. Look at as many swords as you can. And when you decide what school or time period moves you, then go shopping. Until then, keep your powder dry and your mind open. Buying swords is easy. Buying the right sword takes study. Best of luck.