I would definitely recommend a Couch to 5K program as the best way to get into running. www.sparkpeople.com/resource/fitness_artic
Rather than running continuously, these programs work through progressively increasing intervals of running and walking, giving your body time to adapt to the impact of running.
And I echo the advice to keep your running pace down at this stage - you should be aiming at something that is not much faster than a brisk walk. Less speed = less impact. And less impact will probably make running easier of your core as well. Once you are running continuously and comfortably, then you can start working on increasing your speed.