I think the most positive lessons Jeannette learns from her parents were not intentionally taught. Rather, they were perhaps the unsought consequences of living through childhood in "survival" mode with parents who didn't seem to know any better.
First, Jeannette and her siblings learned not to rely on anyone for anything, but instead to be as resourceful as possible on their own. They also learned not to get physically attached to anything that had sentimental or emotional value. Every time the family moved, the children were only allowed to take one important thing with them. For the most part, the children did not make any emotional attachments, and when they did, they learned to treasure something intangible inside them, rather than require something physical to fulful an emotional need.
The children learned how to stand up for themselves and each other. These kids were by no means crybabies, especially with a father who constantly reinforced the lesson that what doesn't kill you only makes you stronger.
We also know, at the end of the story, that no matter what her parents did or didn't do, somehow Jeannette managed to keep her sense of humor. Despite the debateable neglect and abuse of their children, throughout the story it is obvious that Jeannette believes she is loved. It is also obvious that there are as many fond memories of childhood as there are horrific ones. This says that both of her parents, for all their seeming worthlessness, were genuine and sincere in the raising of their children. They maintained a lighthearted approach, always, to poverty and hardship. They made things liveable and fun. Because of this, Jeannette and her brother and sister will always be able to look on the bright side, no matter what kind of difficulty finds them, and likely they will have the attitude that they can survive absolutely anything.