I thought Chicago school would be something like Bud Freeman -> Eddie Miller.
There is also an interesting line going Don Byas -> Lucky Thompson -> Benny Golson.
Early John Coltrane was clearly influenced by Dexter Gordon, but later Gordon showed an influence from Coltrane, which is quite interesting to hear.
And, although Bird didn't record much on tenor, what exists is superior. It is particularly interesting to hear the 1953 Miles Davis session with both Parker and Rollins on tenor, and hear how similar Rollins sounded to Bird.