AI will beat us out of the solar system by far. They'll pack themselves up in Von Neumann probes and go to all the nearby stars at the same time. Then go on to the next furthest stars and on and on and on with some taking the plunge and venturing into the intergalactic void heading to another galaxy.
Our best bet would be to hitch a ride as DNA data. It will be modified on site to survive whatever world they come across, and then grown in tanks. They'll be raised by robots or AI in similar bodies to that of the new humans.
If I had to lay odds, I'd say colon cancer. That sneaks up on a lot of men as they age and is notoriously hard to fight once it spreads. Once it does your 5 year survival rate is 13%. If you catch it while localized or regional, your odds of survival aren't bad.