What sort of fabric could be used for this costume?
The question isn't well-defined, and your list of desired materials isn't clear in terms of how you envision using them.  But based on the picture, I'll throw out some ideas to get you started.  Perhaps you can use this to clarify your question.  Recognize that anything that can't breathe will be really hot, even if it's cool outside.  But a few ideas: 


You might get enough material for the entire costume from a plastic table cloth (or two).  If you get a white one, you can color it with spray paint that's compatible with vinyl.  An unlined, unpainted table cloth may be translucent enough to put lights inside (but they will add to the heat).
A metallic look would be pretty cool.  You can buy really cheap "space blankets" (one or two should be enough, like these).  Any lights would need to be on the outside (maybe LED strips).
If you need costume segments that will hold a simple shape that you can make from a flat material (like a cylinder or surface curved in one plane), you might want to look at drafting vellum, which you can get in large sheets or rolls.  It's made from thin cotton fabric infused with a material like gelatin to make it translucent and stiff.  You could put lights behind that.  It has sort of a plastic looking surface.
For a rubber look, you could use sheets of craft foam.
You can make shaped sections using a lightweight fabric or gauze.  Create a mold for the shape from any suitable material and put a thin layer of a release agent on it, like Vaseline.  Stretch the fabric against it.  Then infuse the fabric with either PVA glue (school glue/Elmers), or hot melt glue.  Saturate the fabric with it.  As you add the glue, work the fabric into the shape if it isn't flat.  For hot melt glue use a heat gun to melt the glue into a thin liquid so it flows into a smooth layer and saturates the cloth.  Let it dry or cool.  Another method is to make a high concentration starch solution, soak the fabric in it until the fabric is saturated, then work the fabric over the form and let it dry.  

The fabric with either type of glue will be translucent.  The starched fabric will look like the fabric. Any of these will retain the shape.
I'm not sure if it fits with the look you want, but Tyvek can look pretty good.  As long as it stays smooth, it has the look of Tyvek.  But it will wrinkle and soften, in which case it will look more like cloth.