Slitherine

I've picked up a load of Achaemenid Persian infantry and I'm not sure how to use them. They are armed with bows, spears and "violin case" shields (I think that's what they are known as). They are Essex figures, MPA 57 (http://www.essexminiatures.co.uk/gal_mpa53.html).
I think these should be Persian and Median foot (MF Protected Undrilled Bow with half Light Spear). However, I think that these BGs would normally be Sparabara, with large rectangular shields and spears in the front rank. How do the archers with violin case shields and spears fit in ? Should I have these in the front rank instead of Sparabara types ? With bow only figures (such as Essex MPA 56) in the rear rank ? Or mix some of these in with the normal archers in the second rank with Sparabara spearmen in the front rank ? Or something else ?

I would go with MPA 56 as the rear rank.

I think that those shields are technically called "dipylon" in Ancient Greek. As I have read in "The Persian Army" (Nick Sekunda, Ed. Osprey), the spearmen represented with that kind of shiled would correspond to the immortals. There are two types of immortal regiments, the one comming from the Persian nobility and others coming from humble origin. You can use those miniatures, along with some archers behind them, to represent the "poor" regiments of Immortals. You can use the MPA 54 for the "noble" immortal regiments.

Regarding the other foot, I would use the squared shield ones for the front rank and the ones with bows for rear ranks. I think these references are the MPA114 and MPA 115.

There is some confusion in the sources as to EAP shields. The shields you have are the 'gerrhon' shield I think. These are shown on the Persepolis place reliefs, for example, which depict palace guards. However, greek art and written sources suggest a much more substantial shield barrier, with mostly bow armed troops behind it. The latter would suggest don't use them as front rank shield wall bases.

However, given that the persian troops in FoG run round the battle field rather than defend a stationary shield barrier I think you could use them for the immortals at least.