Since we also saw Janus VI and Starbase 11, which IIRC didn't have any connection to what Lorca was saying, I assumed that everything Michael saw were references to TOS episodes, and so it was Amerind.
Possible, but none of these were represented by stock footage; they were all "re-imaginings" of those same TOS locations. Plus, Lorca mentions the "Romulan Senate" building which, actually, isn't all that far from what we saw at that exact moment. So it's very possible that Lorca was toggling through the locations of places they had confirmed mycelium nodes existed but only mentioned a handful of them by name. Amerind could be one of them, or one of Andor's moons could have an oddly shaped obelisk that nobody has ever studied in detail.
We have no idea what that chamber was supposed to achieve, only what it eventually did achieve. But currently, a navigator within chooses a target of his liking, supposedly just by thinking of it. Burnham here would probably be doing much the same, and thus everything she sees would be things she already was familiar with.
They hadn't figured that part out yet, though. That transparent chamber is, on Discovery, being used as part of the navigation system: they pump the spores into the chamber, get them good and excited, and then try to push impulses into the chamber that induce them to drag the entire ship to a particular place. Apparently, the crew of the Glenn realized that this process works way better when you have a complex organism like Ripper in the center of it all to act as an interpreter for those signals.
More than likely, the chamber itself is where these experiments started, as Stamets and his buddy originally discovered the mycelium connection through subspace by interacting with the spores under these conditions themselves. They were probably planning to use it for something far less ambitious, like some sort of ultra-long range communication or personal transportation device, but Starfleet was all "Fuck that!" and forced them to develop the system to be able to transport entire starships.
In other words, if Stamets developed the chamber the way it was originally intended, it would basically be an unlimited range one-person transporter chamber. What Burnham was basically looking at was a poor man's iconian gateway, except the device hasn't been really configured to be used that way and it can't really send her anywhere (at least, not anymore) unless the entire ship goes with her.
Of course, without the DNA transfer, she couldn't really go anywhere. Or could she? Why was she impressed by this fuzzy holoshow when her world is full of fuzzy holoshows overall?
Because she knows the difference between bad holographics and matter transfer. In this case, what she's seeing is light being funneled through subspace and into the chamber like images pumped through fiber-optic cables. She can't physically travel to these places, but she can see, hear and smell them in a way that is intimate enough that she knows she is being physically connected to them somehow. It's enough for Lorca to get his point across: Stamets has invented a teleportation booth, and his mission is to adapt the booth to teleport an entire starship.