Does my data automatically transfer over to the new app, or do I have to start all over again?
Your want/wish lists automatically transfer over to the new app. You have to "follow" people in order to get the same lists of stuff gone free/price drops, etc., and you have a wide range of choices so your list can be even bigger/more far-ranging than in the old app. The Appshopper Social official thread should give you some good ideas and recommendations on how to use the new app.
P.S. The website and the old app are working again.