How to deal with reflections in a space helmet
The best thing you can do is get as much right on set as possible. Cover cast, crew, and equipment with black fabric, hide them behind black curtains,  Get your talent as far away from the green screen as far as you can while still maintaining its utility; choose your angles carefully, and keep the shots short, because whatever you do, you're going to have to fix something in post. In a perfect world, all that would be would be the key, but the world is never perfect.

Additionally, you might consider removing the plastic visor and adding it back in post.   You'd need to capture clean plates and a mirror ball on set, so that you can re-cast the reflections on the visor (after photo shopping out cast and crew, etc) . Then you'd use object motion tracking and (if your camera moves) camera motion tracking to insert 3d geometry.where the visor should be. This approach removes some of the complexity of keying a spherical, reflective surface, but adds complexity with the motion tracking, which can really mess up your shot if the solve is even a fraction of a hair off.

In any case, don't underestimate the complexity of what you're trying to do. Hire a qualified person or persons to do the work if you have the budget. If you don't, make sure you test your workflow thouroughly before you commit.