You would be correct in asserting that many crusaders would not have possessed swords, as their relative expense would prohibit many of the less wealthy ranks of society from owning them. The spear, and to a lesser extent, the axe, would have been more ubiquitous weapons among the ranks of the crusader host.

However, among the knightly ranks (and whoever could scavenge one from the dead etc), swords were more common and heavily used in battle, although less feared, amongst their enemies at least, than the couched lance charge for which the Frankish knights became famous. These swords would hardly have been standardised in pattern, but the relative types have been categorised in what is known as the Oakeshott Typology, recording the relative eras and dimensions of various blades.

For the First Crusade, the Type X, Xa, XI, XII are considered widespread by the Oakeshott typology. For a quick rundown, the Type X (and Xa) was a leave-over from the Viking Age, a broad, flat, choppy blade (roughly 80cm in blade) with a relatively narrow guard about 20cm wide and with an oval or disk pommel. The XI was a development from this, originating around the start of the Crusade, for fighting from horseback, with a slightly longer, more slender blade, while the XII had a shortened fuller, a slightly wider guard, and was more tapered, resulting in improved thrusting characteristics. As such, the First Crusade, and the era around it, can be considered a 'transitional' period, as swords and armour began to change alongside each other, increasingly heavier armour demanding that the relatively settled style of the Viking-era blade (dealt with by the Petersen typology) shift to become larger, heavier, and increasingly more pointed to deal with it.

I hope that this helps answer your question. For the relative typologies of swords, I suggest you consult:

Ewart Oakeshott, The Sword in the Age of Chivalry, (Boydell, 1994)

Oakeshott, Records of the Medieval Sword, (Boydell, 1991)

A translation of the typology of Dr Jan Petersen is available here: http://www.vikingsword.com/petersen/

(and if the link doesn't work just search his name on wiki, there's a link there)

From a slightly later period (from before the second crusade to a few years before the third), but an interestingly 'on the ground' account can be found in Usamah ibn Munqidh's kitāb al-i'tibār (online as of fairly recently, I'd advise you to check your library for the more recent translation by Paul M Cobb first, though this one's pretty good too). It's essentially a collection of anecdotes (mostly taken from his own life) about hunts, battles against Muslims and Crusaders, holy men and so on.

Almost all Usamah's anecdotes about war are focused on mounted combat of upper class men armed with lances. In this context swords were very much secondary weapons (though it seems everyone is armed with them), and he records an occasion where he found himself on his own and

I had no weapon except my sword. The Arabs made an assault on me, but I found nothing with which to repulse them, my horse was incapable of carrying me outside of their reach, and their lances were already reaching me.

Despite being a bit of a weapon of last resort while mounted, the sword seems to be essentially the primary weapon while dismounted, whether in executions or assaults on fortifications. Swords could inflict some pretty unpleasant wounds: particularly on people wearing little armour as when

The Ismā'īlite held in his hand a dagger, while al-Ḥājj held a sword. The Batinite rushed on him with the knife, but Hammām struck him with the sword above his eyes. The blow broke his skull, and his brains fell out and were scattered over the ground. Hammam, laying the sword from his hand, vomited all that he had in his stomach, on account of the sickening he felt at the sight of those brains.

It's a fairly interesting book, but it only really answers your first question. Most people other than the military elite that Usamah was one of are rather invisible in the book. You can see a few points here and there that shed a little light on the second question (men armed with daggers, or completely unarmed, or occasional mentions of slightly lower class people with swords), but it doesn't come close to properly answering it.