Sorry for the late response, with the holidays and all this was pushed back on my to-do list.

The closest source I have in front of me is the Taktika of Nikephoros Ouranos, written in the early 11th century. Given that the First crusade took place in the late 11th century the information could be 50-100 years out of date. Given the slow pace of military technology during this period I do not believe the equipment would have differed much between these periods. To give one example, the Praecepta militaria of the Emperor Nikephoros II Phokas, written in the 960s A.D. does not differ in any way from the Taktika written ~50 years later in terms of foot soldier equipment.

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

Sources:

Praecepta militaria Nikephoros II Phokas

Taktika Nikephoros Ouranos

Sowing the Dragon's Teeth Eric McGeer