Have you tried connecting the backup drive, and then using Migration Assistant?
That's just what it was designed for.
Special note regarding iPhoto:
If you're now on El Capitan, versions of iPhoto earlier than 9.6.1 won't run. (Photos runs instead).
You CAN still use iPhoto, but you need to do this:
a. Once everything is set up, delete the old iPhoto app from your applications folder.
b. Sign in to the Apple Store and re-download iPhoto.
c. Apple store should send you final version of iPhoto (9.6.1) which DOES work with El Capitan.
(this doesn't work unless you delete the old version FIRST)