This is in reference to common footsoldiers/light cavalry; I am aware of the fact that knights and nobility could have drastically individualised equipment, however what interests me is whether any specific nobles/kings tried to standardise equipment for all of their soldiers, comparable to that of the Roman post-Marian troops or of 18th century line infantry. Thanks in advance.
Actually, yes!
(NB: This is borrowing heavily from Simon Coupland's really solid article on Carolingian Arms and Armour at the De Rei Militari site.)
In the Carolingian Empire, there were several attempts to standardize the weaponry carried by soldiers, if not the quality of it. For example, the capitulare missorum of 792-793 instructed those landowners who were fighting to bring horse and armor, as well as shield and lance, longsword and sax. A letter sent by Charlemagne to Abbot Fulrad in 806 also ordered each horseman to have a bow and several quivers of arrows in addition to the shield and lance, sword and sax, indicating a differentiation between (presumably) heavy and light cavalry, respectively.
The Capitulary of Aachen, issued in 802-803, expected the counts to supply each of their foot-soldiers with a shield and lance as well as a bow with a spare string and twelve arrows, and a further provision that no soldier should carry a cudgel, presumably as an admonishment to those who didn't have a lord wealthy enough to provide a spear and shield.