What did those who walked the First Crusade wear? I'm not just talking about the noblemen etc. but also the poor people who allegedly went (or is that a myth?). And how did they dress according to their own fashions/standards/habits once on the road? It took them quite some time to get to Jerusalem so I'm thinking that at some point they've had to get new threads?
I'll cover just the peasants. Peasants participated in the First Crusade in three ways. First, in the very poorly organized People's Crusade preceding the First Crusader armies by a few months. Second, peasantry would made up the bulk of the armies raised for the First Crusade and most would simply be wearing their normal work clothes. Third, camp followers, specialists, craftsmen accompanied the Crusader armies.
These people would likely be wearing what they normally wore for traveling and working. Many had no idea how far away Jerusalem was or what the climate would be like.
A typical 11th century peasant traveling outfit would include a blouse of cloth or skin, a leather belt around the waist, a long wool mantle over the shoulders, a hood, a knife, and a purse. Some would wear trousers, some would wear a smock. If they're lucky they had hose with shoes or boots, but many would be barefoot. Underwear was not a thing at this time.
Men harvesting, from an 11th century Anglo-Saxon calendar. Source
What did they do when they wore out? They patched them, and patched, and patched. When their shoes wore out they patched them too, then they went barefoot. Eventually the People's Crusade would do what most undisciplined and undersupplied armies in the field do: steal, loot and pillage. Since they spent most of their time in European territory this didn't go over so well.
The People's Crusade never made it to Jerusalem. It was destroyed shortly after crossing into Anatolia at the Battle of Civetot. Of the tens of thousands who set out, a few thousand survived and returned to Constantinople. Some joined the official Crusader armies and continued with them to Jerusalem.
Peasants did not participate in the first crusade, at least in the way that this question is implying. Pope Urban II called for the noblemen or knights to go and recapture the "Holy Land." In exchange for their service, the Pope granted a "plenary pardon" to all those who participated in the crusades. Peasants began to participate in the later crusades because they wanted the Pope's pardon as well. When hoards of peasants began to trek over to Jerusalem, wreaking havoc in their wake, the Pope began to grant the pardon to people who would help sponsor a crusade, in an effort to keep peasants from crusading themselves. Peasants during the first crusade would be apart of a knights entourage. These people were extremely poor, and wore a blouse and britches. When these clothes wore out, they would keep wearing them, because it was all they had.