El Capitan and old iPhoto backup
Photos will read the iPhoto database and tell you if the old system is too old. In that case, you'll need to download a tool to fix the library or upgrade iPhoto.

You certainly don't need iPhoto on the new mac unless you a) want it b) it helps you in upgrading an old library.

Basically, don't erase the old Mac or backups and jump in. We're here if you run into a specific error in the process.