When is it best to transfer data to my new phone (Samsung Galaxy A3 from Sony Xperia Z5 Compact), before or after activating the new phone, or doesn' t it matter?
It doesn't matter, although if you activate the phone and enter your Google address (use the same one you used in the A3, and it's an existing account, not a new one), it will sync a lot of things, like contacts, calendar, pictures, etc. Then you can transfer anything it didn't sync.