I compiled a list of equipment for a 10th/11th century Roman Byzantine army for a previous question, I'll copy it here to hopefully give you one perspective. Unfortunately, I cannot comment on the equipment of western European armies.

In terms of time period, the sources I am pulling from are the Taktika of Nikephoros Ouranos, written in the early 11th century and the Praecepta militaria of Nikephoros Phokas, written in the 10th century,

All quotes and information below are from Praecepta militaria and Taktika.

At the time of the Taktika, there are 7 types of soldiers outlined in the text. Foot soldiers, archers, javeliners, slingers, menavlatoi, kataphraktoi and prokoursatores.

Foot soldiers

• short tunics extending to the knees, of cotton or coarse silk;
• short boots folded up to the knees or unfolded up to the thighs;
• thick caps of felt fastened over their heads with bands of cloth,
• sword, axe, or iron mace. Stored at the waste on a belt.
• sling stored in the belt.
• Shields no smaller than six spithamai, larger if possible
• thick and solid spears, from twenty-five to thirty spithamai in length. Nikephoros Ouranos: "Their points and fastenings should be fit for the task."

Archers

• fifty arrows each in their quivers
• two bows
• small shields
• extra bowstrings
• swords or axes
• slings

Neither Praecepta militaria nor Taktika gets into the equipment of the slingers and javeliners, only their tasks and positioning. Archers and spearmen were the primary infantry force and the slingers and javeliners only had a supporting function. This is one explanation as to why their equipment is not detailed.

Menavlatoi, the Menavlatoi are an interesting type of soldier and their equipment is hotly debated. The text states: "[the Menavlatoi] must have thick menavlia with a length of one and a half or two ourguia while their points must have a length of one and a half or two spithamai, so that, when battle begins, the units will calmly move out through the intervals and engage the enemy.". The maneuver Nikephoros Phokas is describing is when heavy cavalry are preparing for a charge against the Byzantine formation, the Menavlatoi take position in front of an extra rank of spearmen (for a total of 3 ranks of spears + 1 rank of Menavlatoi) to stand firm against the cavalry charge. Their purpose, along with the description points to some type of pike or halberd, maybe a bill sort of weapon. Regardless of what it was, it was the front line of defense against a heavy cavalry charge.

Nikephoros Phokas continues: "All the javeliners and menavlatoi should have shields smaller than those of the [foot soldiers]". "Their menavla must not be made from wood cut into sections but from saplings of oak, cornel, the so called artzekidia, of from another hard wood. if trees in one piece cannot be found, let these menavla be made from trees cut into sections, but they have to be of hard wood and as thick as hands can wield".

Prokoursatores are light horsemen and Nikephoros Phokas states, "must be proficient archers". Nikephoros Phokas does not go into their equipment with much detail but we do know a few things:

• klibania
• helmets or lorikia
• swords or maces
• Bow and arrows are not mentioned, but "proficient archers" infers they are armed in such a fasion.

kataphraktoi or lancers. These are heavy cavalry, an equivalent to a medieval knight although the rider and mount wear considerable armor.

• shields, more modest than those of the heavy infantry. Of either four or five spithamai.
• klibania with sleeves down to the elbows.
• arm guards and leg guards of chainmail, coarse silk or cotton.
• Over their klibania they should wear epilorika or a shirt of coarse silk or cotton.
• Iron helmets which cover their faces with chainmail, two or three layers thick so that only their eyes appear.
• The horses must also be armored, either pieces of felt and boiled leather fastened together down to the knees so that nothing of the horse's body appears except its eyes and nostrils likewise their legs below the knees and their undersides should remain uncovered.
• The horses can also have klibania made of bison hides split at the legs so that movement is not impaired.
• swords
• maces with all iron heads, three, four or six corner varieties with sharp corners.
• lances

definitions:

• klibania: waist length curiass, usually of scale armor
• lorikion: waist length mail shirt worn with padding
• ourguia: unit of measure, about 1.8 meters
• spithamai: unit of measure, ~24 centimeters

Edit based on /u/Alpy94 's clarification

The Byzantines of this period fought in a square formation where infantry of all the types described above worked together to form a mobile base for cavalry based attacks. The formations consisted of 12 units, three per facing. The units were spaced out such that cavalry could move freely into and out of the square as the battle required. Each unit consisted of 2 ranks of foot soldiers or "hoplites", 3 ranks of archers, then 2 ranks of foot soldiers. In the event of a frontal attack, one of the rear ranks of foot soldiers could move to the front of the unit. In the event of a cavalry charge, Menavlatoi in reserve would also move forward changing the formation to:

• Menavlatoi
• Foot soldiers
• Foot soldiers
• Foot soldiers
• Archers
• Archers
• Archers
• Foot soldiers

After the charge connected, the javeliners and slingers in reserve would assist in driving the attackers away.

To quote the text directly,

The formation of the infantrymen under discussion is to be a double-ribbed square, thus called "a four-sided formation" by the ancients, which has three units on each side so that all together there are twelve units on the four sides. They must be set apart, to the extent possible, to allow space for twelve to fifteen cavalrymen in each interval so that the combatants can move in and out.

In each interval was a unit of javeliners, slingers, archers, and Manavlatoi who are tasked with driving back any attacks into said intervals.

The structure of each unit is described as folows:

The taxiarchs are to have under their command four hundred heavy infantry and three hundred bowmen, so as to make up one taxiarchy, which, as explained above, is double-faced, keeping two infrantrymen in the front and two in the back, three bowmen must be stationed between them in order to make up one division out of the twelve divisions. The taxiarchs should have another three hundred men to make a full complement of one thousand, of whom two hundred are javeliners and slingers and one hundred [Menavlatoi].

As far as the cavalry the light (prokoursatores) and heavy (kataphraktoi) are divided into banda of fifty men, each led by a droungarious. The cavalry units were more homogenous but not entirely so. The prokoursatores operated together, as scouts, skirmishers, and to pursue fleeing enemies. The kataphraktoi were deployed in a triangular formation described in great detail by the sources. (Seriously, they go on about it for pages and pages). The general idea of the cavalry triangle is as follows,

• first four lines were to be composed of kataphraktoi with iron maces
• from the fifth row to the twelfth, the outer kataphraktoi on either side were armed alternating with lances or maces/sabers.
• from the fifth row to the twelfth, in the middle of the formation, were mounted archers
• the formation's first row consists of twenty men, and increments by four each rank. e.g. 20, 24, 28 etc. for a total of 504. Of the 504, 150 should be archers.

I have taken some pictures of diagrams I hope will be helpful and uploaded them [here] (http://imgur.com/a/SVwsE)

In conclusion, this is only one example from the Medieval period but I hope it illustrates that Byzantine armies were organized in rather complex ways and while certain units may have been homogeneous for specific purposes, many were not. The sources emphasize the army working together as a formation, rather than individual units segregated by equipment functioning independently.

Sources:

Praecepta militaria Nikephoros II Phokas

Taktika Nikephoros Ouranos

Sowing the Dragon's Teeth Eric McGeer

edited again for clarity

My first gold! Thank you!

Follow up related question:

In feudal levies, where there requirements what you had to bring when called? Or did some guys show up with a bow, another with a spear etc. all willy-nilly. Or was there some kind of agreement/organization that x number of pre-decided people brought bows, x brought spears etc. I'm thinking mostly of peasant levies, not knights and the nobility.

In addition to /u/sunagainstgold and /u/mrleopards fine posts, allow me to briefly discuss Anglo-Norman and Angevin army organization in the 11th-12th centuries. If you're interested in a more detailed examination, I cover it in more depth here.

A hallmark of Norman warfare was a preference for flexible, all-arms armies composed of infantry, cavalry, and archers. But our sources for the Norman Conquest (which are not great for the purpose) show us no tactical division beyond that, and even these were somewhat fungible. Knights, for instance, were equally comfortable fighting on foot as they were on horse. William of Poitiers distinguishes between archers and infantry at Hastings, but the Carmen de Hastingae Proelio does not. William is probably right, but the disagreement raises questions. Were archers not tactically distinct from infantry yet? Did they comb archers out of infantry companies to form ad hoc units? It's difficult to say.

By the late 12th century, the combined arms formula had become more refined, though there was still no subdivision beyond infantry/archers/cavalry. The army that Richard I took to Palestine was a surprisingly sophisticated instrument which depended on close cooperation between arms and twice defeated Saladin in open battle. Blocks of heavy infantry screened the army and absorbed Muslim arrows with their shields, mail, and padded or felt armor. Crossbowmen shot their bolts from between the blocks or around the flanks and kept the enemy at distance, or bled him if he came closer. Cavalry filled the role of tactical reserve, kept behind the infantry for the purpose of delivering a decisive blow when the time was right.

Certainly, we could expect to see a preponderance of certain arms, but that has more to do with cultural preferences, economics, etc than commanders being OCD. The spear was undoubtedly the most common weapon of the infantry. But no one was going to turn down a trained man if he showed up with an axe or a sword. The fighting men made the army, not the other way around, and so the composition of the army was essentially dependent on what the soldiers already possessed.

Follow up question, were separate/specialized units required to acquire and maintain their own equipment? If so, was there any attempt to standardize or otherwise assure uniformity of quality and type?