>I'm willing to take that chance for future generations

All of recorded human history would not cover 1/10 of the time this journey would take. Being optimistic, I would hope that whatever we send today would be considered beyond an ancient, obsolete relic before it arrived at a black hole.

Additionally, the speed of this probe is actually the easiest problem. Then it has to be constructed to endure the massive gravity that will tear it apart on a molecular level. Then, we have to figure out how to transmit any data back from something that doesn't let light escape.