Would it be best to walk around with sciatica or rest?

Be careful: You should stay active but try not to do anything that expressly worsens your sciatica. Sciatica is mostly the result of a disc herniation or an annular tear in the discs of the spine and by keeping a high level of activity you run the risk of injuring the disc more.

Rest Not Recommended: Always good to stay active as long as it doesn't make your pain worse. Too much rest makes things worse for sure. Usually it resolves in majority of patients within a fews weeks, if longer than that consider seeing your doctor.