the arm pictured (looks like Hyde's arm from League of Extraordinary Gentlemen, btw) is likely a fiberglass shell covering the mechanics with (thinking back to the era) likely a foam latex prosthetic sleeve over it, painted up and with punched hair... the same could be accomplished today with a thin silicone arm backed with a mesh sleeve over the fiberglass shell...
Each method has its pros and cons, being foam latex can be purchased relatively cheap and there's a wide array of paints that can be used to paint it but the foam requires baking and can be tricky being mixed as it is sensitive to environmental factors and can come out extremely soft and pliable or very dense according to how its mixed and the different elements added (sounds trickier than it really is, you just need to watch it) Also foam latex required casting materials that are porous and can handle the heat of baking. Silicone is relatively easier to use and cures on its own, but the pigments used can be pricey (so can the silicone, for that matter) and you can only use specific types of pigments... Silicone can also look much more realistic if painted correctly. you can also use fiberglass for casting, which makes your molds so much lighter and easier to manage. Silicone Is also much heavier than foam latex, so that's also a consideration.
Of course you could also go with slipcasting latex over a soft polyfoam base, which wouldn't look as realistic up close, but would be quicker than foam and lighter than silicone... and as long as you've got a solid sculpt and a good mold, it should work... might also take some trial and error to get the mechanics to work right in the polyfoam...
So it's cost vs function, basically, plus your own personal technical skill level... Everyone? Did I miss anything?