Would there have been any expectations or requirements as to how the nobility or soldiery were equipped or dressed, beyond simply what they could afford? Did the soldiery in any way replicate their lord’s heraldry, once that became a thing? Were there weapons exclusively meant for one tier of fighter vs. another?
Well it depends, on era and country. At least I can give you an answer for the late 15th century Holy Roman Empire. Prior to the burgundian wars, the urge for uniformation started, due to the refomations of the military by Albrecht Achilles prince elector of Brandenburg. The emperor Friedrich III. ordered Albrecht to elaborated the possibilites of a standing army and the raise of it, due to the threats of the ottoman empire and the duchy of burgundy. When the burgundian declared war on the empire in 1474, imperial troops were levied. And the imperial cities, duchies etc. ordered there troops to wear red jackets, with one white and one dark stripe on one sleeve and oak branches on their helmets and hats, to identify the troops. The burgundian troops were identified by a red andrew cross.1.
The swiss mercenaries wore a white cross on their clothes. 2.
The amount of armour and weapons depended on the income of the levied troops and the region, atleast in the territories of the HRE. The weapons and armour varied a lot by the areas. Shields weren't use in middle and north germany, in the south it was a common weapon for example.
A minium requirement were a form of a pollweapon or missle weapon, and a helmet, depending on the territory of the empire. the troops of the village Bollstedt for example had to wear a helmet, chainmail armour, a jacket and used a crossbow. 3.
sources:
1.Aarau, Aargauer Kantonsbibliothek, MsWettF 16: 2, f. 58r – Silbereisen: Chronicon Helvetiae, partie II (https://www.e-codices.ch/fr/list/one/kba/0016-2)
2.Aarau, Aargauer Kantonsbibliothek / MsWettF 16: 2 – Silbereisen: Chronicon Helvetiae, Teil II / f. 173r