One famous one, and a good starting place, is The Alexiad, Princess Anna Komnene's biography of her father, the Emperor Alexius I. Alexius I's reign, 1081-1118, neatly covers the First Crusade, and the author writes about her father asking the West for aid, the arrival of the Crusaders in Constantinople, the Crusaders falling out with her father, and the events of the First Crusade. All primary sources are biased, of course, but the Alexiad rather more so than most because Her Imperial Highness is bound and determined to portray her father in the best light possible. Nevertheless, it contains firsthand accounts from a woman who actually met many of the protagonists of the First Crusade as they passed through her father's court.

I remember reading a book with the translated account of two crusaders, John de Joinville and Geoffrey de Villehardoin. Geoffrey wrote about his experiences on the Fourth Crusade, while John was on the Seventh. Hope that helps a bit.

I'm sorry to ask this, but why make this harder than it is? I don't know your situation, but I assume you are taking some sort of history course? Undergraduate historical research starts with reviewing the sources of published historians. Look at a book by any crusade historian of note in the last 30 years (like Jonathan Riley-Smith, Jay Rubenstein, Thomas Maier, Bernard Hamilton, the list is endless.) published by an academic/university press and turn to the bibliography. Primary / original sources are often listed separately.

For example, Riley-Smith's The First Crusade and the Idea of Crusading has 6 pages of cited primary sources. Rubenstein in his Armies of Heaven: The First Crusade and the Quest for Apocalypse even includes a short bibliographic essay on the chief primary sources of the first crusade!

The above is more than sufficient for starting any undergraduate essay.

The Council of Clermont, in 1095 AD is where Pope Urban II made the first call for a crusade to the holy land. There are five surviving accounts of Pope Urban's speech. All five can be found in the Internet Medieval Sourcebook of Fordham University. http://legacy.fordham.edu/halsall/source/urban2-5vers.html

Ambroise's The History of the Holy War, translated by Marianne Ailes was written in rhyme which makes it quite an interesting read. I don't speak French but I know there are online copies of the original. The source only covers the Third Crusade, so may not be what you're looking for.