Ain't what They Used To Be, Frolic Sam, and Good Queen Bess are just a handful of titles that will work for you. I understand Jazz at Lincoln Center is currently publishing the Essential Jazz Editions, which feature seminal jazz music starting with New Orleans Dixieland charts such as Tight Like This, and Tiger Rag. The second set is just off the presses and features the music of Louis Armstrong with his Hot Fives and Hot Sevens. Contact Nyala for more information. That is a hard one to answer without knowing the specifics of your school.
Some auditoriums are better than some rehearsal halls.
What it comes down to is finding the right location where you can capture the acoustic sound of your band with a minimum of trouble. We are not looking for tapes that sound as though they were recorded professionally. In the old days, they used to hang a couple of microphones over the band, and let them play, with no mixing, no amplification, no nothing. That is still the best way to do it, but it takes some courage to let the band balance itself, and not to go in for any gimmicks or anything even slightly artificial to boost the band's sound. As far as the recording equipment, do the best you can - we can deal with it.