Getting induced 37 weeks

I'm a FTM currently 33 weeks and found out I'm getting induced at 37 weeks due to gestational hypertension. What should I expect in regards to labor and my baby's health? Also is there anyway to attempt to go into labor naturally the days before the induction or is it too early to hope for that? Should I wait to have visitors until her original expected due date or longer? What was your experience? We're planning on atleast waiting until her due date for visitors which means no hospital visitors either since she'll be late preterm in the peak of flu season, also my family generally gets sick around this time.