There isn't too much recorded music of this time because recording technology hadn't quite been invented. The video is of King Oliver, whom we'll get to tomorrow.
Within New Orleans, Storyville (aka The District) was where all the jazz was happening from the late 1800s through about 1917. Storyville was a very popular place because of all the brothels located so closely to one another. The best brothels were the ones that had the best musicians which meant there were always jobs available. However, because playing in a brothel was looked down upon, many of the those who did play in brothels never admitted to it. After a time, the brothels in Storyville were shut down by the Navy because too many sailors were getting STDs.
Jazz instrumentation of this time is similar what we see today, with some distinct differences. The front line typically consisted of coronet, clarinet, and trombone. The coronet is very similar during to the trumpet and for whatever reason, was much more popular than the trumpet during this point in American music history. The coronet has a more mellow sound than the trumpet and typically had the role of playing the melody/lead in tunes. The saxophone had only been invented about 50 years prior and so the instrument of choice for reed musicians was the clarinet. Because the clarinet has a higher register than the coronet, this instrument would take on the role of embellishing the melody which included arpeggiating around it. We don't see trombones too often throughout jazz bands, but in early jazz their role was to provide lower harmonic counter melodies.
Early rhythm sections were comprised of tuba, banjo (rarely guitar), piano, and a percussionist. I say percussionist instead of drummer because the drumset as we know it today had yet to be fully established. Drumsets of this time had a very large bass drum (taken from brass bands), a hi hat, a snare drum, and perhaps another cymbal. No sort of toms were used. In the early days the tuba would take over the role of the bass player in providing the roots of the chords for the rest of the musicians to base their pitches on. The role of the banjo and piano were simply to provide harmonic and rhythmic information to the rest of the band.
"Hot can be cool, and cool can be hot, and each can be both. But hot or cool, man, jazz is jazz." - Louis Armstrong