I am not qualified enough to answer for the leadership of the crusaders, nor the participation of women. I can however answer about the equipment to a reasonable degree, and so that is what I will do.

As you know, the People's Crusade happened in the late 11th century, more specifically in 1096. In this time period there is actually very little to speak for a 'common mans armour' so to speak. The most common form of armour in europe during this age would be mail, and this type of armour is referred to in many sources both before and after the 11th century. Examples being Beowulf, Viking sagas and plenty of other sources. Plenty of finds and visual depictions of this kind of armour as well.

Now mail however would not have been something cheap, and not something most peasants (freemen or not) would have been able to acquire. This research puts the price of a mail shirt at 100 shillings. Now this is later than the specified period, however it does serve as an indication on what we can expect.

What is scant however are any mentions to any kind of armour that would have been affordable to commoners. Not only are there not any mentions of this, but visual sources such as manuscripts and illustrations of the time depict fighting men in little but tunics. It is not until a while into the 12th century where we both see sources and depictions of quilted armour, known today most commonly as 'gambeson', that start to become commonplace.

What there's both mentions and depictions of however are shields, and the majority, if not all, would have had at least a shield. Spears were also common weapons. Interestingly enough, many depictions that depicts warriors fighting without armour still has them using swords. There's a case to be made on how far you can trust art, and I myself don't have many other sources to either back up the idea of swords being commonly used or disprove it from this period.

Now this is by no means a concrete answer, but I wrote it to provide a perspective.