The older type is a scale corslet of the same general sort used in West Asia for centuries. According to archaeological finds, Persian scale was mostly iron and sometimes bronze. Xenophon describes Persian cavalry wearing bronze thorakes, but doesn't explicitly describe them as scale. A cavalry commander named Masistius is reported to have worn golden scale (presumably gilded iron, which would be protective but resist rust) under his tunic (Herodotus IX.22). If wearing scale under the tunic was standard practice, perhaps to keep the sun off the metal, that could account for the lack of scale portrayed in period art, even among the presumably elite guards of the king in imperial reliefs.
If earlier Mesopotamian art is any indication, it's likely the Persian corslet had short or no sleeves. Anyone looking to replicate one might look to the work done by Sean Manning. It is a massive undertaking.
The Persians and Scythians also sometimes used Greek-style corslets. The type has been widely known as the linothorax ("linen chest"), which is actually a term from Homer, though references to thorakes of linen exist in Classical literature. In fact there is no clear evidence linking the style of corslet to linen construction, and a competing theory has emerged linking the style to the term spolas, indicating hide (probably leather) construction.
Some long (but worthwhile!) threads at RAT have examined the literary and artistic evidence, cost and protective qualities of quilted linen, glued linen and leather in the style. One outcome of the discussions is that the style is increasingly referred to as a "tube-and-yoke" or T&Y corslet/cuirass, since the fact that it was made out of a tube around the body and yoke over the shoulders is the only thing that can be said for certain about it.
As for what it all means for us: To be honest, I haven't done enough research on the experiments many reenactors have performed to recommend what the new XMFM member should use if you choose to wear a T&Y. The tentative rule will be that you may use any material that could plausibly have existed in the period and demonstrably provides decent protective qualities. (That is, if your corslet is no more going to save you from a spear thrust than a motorcycle jacket would, you need to go back to the drawing board.) Keep in mind that the two options aren't mutually exclusive: It's not impossible, given what we know, for some T&Ys to have been linen and others leather.
After the Graeco-Persian wars, the T&Y was sometimes reinforced with scale, usually around the midsection.
Upon the head
Next time: If I am not shield...