Yeah T-bug is your netrunner and the girl in the Militech training chip she has hacked and augmented. You meet her first for this job, actually in the training sim, and she is running scans/making hacks for you in the mission for the first time. You are all three part of a crew being assembled for a job (which at this point you know nothing of) - Jackie is your usual partner.
For Nomad, once your "smuggling the lizard" goes wrong you agree to set up with Jackie - which leads to a montage of 'first seeing the sights', meeting mum, getting drunk, stealing a case, making a sale etc meeting misty, losing a tooth, chasing bad-guys, having a shoot out, meeting mum and misty, moving into a new apartment ... then in the car getting your new job... do you want tutorial on how to play?
For Street Kid... once your "steal the hot wheels" doesn't quite head the same way everyone expects... the rest as above.
For Corpo-rat... once things go sideways... Jackie takes you in... rest as above. I think this one is the longest of the intro missions though, but only by a bit.