My wife and I each have an iPad and iPhone synced via iCloud. We would like to have different apps, so what settings are required to ensure that some apps on my wife’s devices can be deleted without affecting my apps? We have used the same Apple ID to obtain apps and the same iCloud account during previous settings of the devices. Should my wife have a different Apple ID, using her email address, then which settings should be changed?
Doug is right, it is more straightforward if you each have your own Apple ID but whoever has the new one will lose access to any paid-for apps bought on the existing one.
You could set your phone not to download purchase to all devices. If your wife deletes an app, I don't think it will delete it from your phone but if it does, download it again - there's no charge. But remember to turn off download to all or your wife will get it back!