A semi-transparent material that is a solid I am trying to find something I can get the ingredients for and make that starts out a liquid and sets into a solid. My end goal is to create a simple 8bit art figure so I want to pour it into a mold and have it harden. Also I would really like something fully or partly transparent (I was looking at aerogel because of the nice blue translucency but it seems too brittle to work with). So my question is what would be the best compound to try to create this figure out of?
There are other plastics that have better mechanical properties, but probably nothing is easier to find than polyester casting resin. It works really well in silicone moulds and there are various pigments you can buy to change its colour and opacity. It isn't as optically clear as some polyurethane or epoxy resins (you won't be making lenses out of polyester), but it's not bad and you can find it in a lot of art supply stores.

As for something with aerogel's smokey translucency, I don't know. Aerogel's translucency (its colour, as well) is due to scattering off its nanoporous structure. It may be possible to mimic the look by blending silica particles or something into a plastic to cause scattering, but I can't recommend anything specific.