R:TSC mentions little about the crew of the SDF-3, since those details are not pivotal to the story. We know that Admiral Rick Hunter is aboard her, and Maia Sterling mentions that most of her family is aboard the ship. A deleted scene implies that Doctor Emil Lang is aboard either the SDF-3 or the Deukalion at one point in the story.
As middyseafort mentioned, the prequel comic mini-series adds more details to the story, but as many Robotech fans know, the story details in comics don't always jibe with the animated stories. Although I enjoyed the Prelude mini-series, I consider it more "what might be" than "what is."
If you are interested, the mini-series describes such events as the change in appearance of the SDF-3, Lisa's whereabouts, the fate of Breetai, Exedore, the Invid Regent and Lynn Kyle, as well as the whereabouts of Lynn Minmei and Dana Sterling.
As middyseafort mentioned, the prequel comic mini-series adds more details to the story, but as many Robotech fans know, the story details in comics don't always jibe with the animated stories. Although I enjoyed the Prelude mini-series, I consider it more "what might be" than "what is."

If you are interested, the mini-series describes such events as the change in appearance of the SDF-3, Lisa's whereabouts, the fate of Breetai, Exedore, the Invid Regent and Lynn Kyle, as well as the whereabouts of Lynn Minmei and Dana Sterling.