Their original mission was to stop SkyNet, however, now they're doing both trying to stop SkyNet and save people. The reason they save people is linked to your later question.
Sarah and John have killed the people that created SkyNet once. However, when the show starts Cameron pops up and tells them they didn't stop Judgment Day they just delayed it several years and SkyNet is created by other people. Namely other people that were directly or indirectly involved in the original program.
So that's why I think they're saving people, if SkyNet is going to happen anyway, we need to save "our" people.
The show is leaning toward you can't stop Judgment Day from happening.
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La Disciplina È La Mia Spada,
La Fede È Il Mio Schermo,
Non salti Ciecamente In Incertezza,
E Potete Raccogliere Le Ricompense.
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