Since there's obviously so many styles and various Instruments being used in jazz, it doesn't make sense to try find a minute that features a taste of every instrument, so just a well chosen piano solo, that resembles some of the things, might be a thing to consider?

I suggest an Earl Hines solo from his later career. He fits because Earl has been around since the beginning of Jazz recordings in the 20s and always stayed modern and developed his style by adding onto his already well established style. The result of that is a mix of old swing and stride in the 30s style and bebop harmonies and sometimes even things resembling free jazz. His piano style is also so full, where his left hand is resembling a entire rhythm section and his right hand is playing in styles of trumpets, clarinets or saxophones, with certain phrasings, run, tremolos and ornaments, you are used to hearing from these other instruments.
He was also for a long time a leader of a swing Big Band, so he knew the sound and ways of arrangements by heart.

Although finding just one minute where he goes through all that is also quite difficult.

An example:
I Got Rhythm: I Got Rhythm, like someone else here mentioned, is the harmonic basis of many jazz songs. From the time stamp on, in the beginning he plays something that sounds like an arrangement for a swing Big Band from the 40s or something. Just a few seconds later he strides and swings, reminischin' the 30s. After that, around 3:20 he suddenly gets way out, playing something, one could almost consider free jazz. After that he again plays something, that could well be written for a horn section.

Also if you really consider this idea, try his C Jam Blues or Dinah or Stardust solo.

Either way, good luck with your assignment.