Apple's 6 pages of exhaustively meticulous step-by-step instructions: How to move your iTunes library to a new computer - https://support.apple.com/HT204318 Use this if you suspect any of your media are not in the standard location (iTunes Media folder).
My one-sentence summary if you always use iTunes' default preferences settings: Copy the entire iTunes folder (and in doing so all its sub-folders and files) intact to the other drive, hold down the option/alt key (shift on Windows) while starting iTunes, and when requested to select a library select the iTunes Library.itl file in the copied folder (Open a different iTunes Library file or create a new one - https://support.apple.com/HT201596).
As for the iOS backups that's another matter. You can just move the backups to the external drive and then should you need them copy them back to their location on the internal drive where iTunes will look. Some people try to automate the process by using symbolic links to get iTunes to use a different location but recently there have been posts about this not working. I haven't tried it so I don't know if that is universally not working or just a few people with issues.
Locate backups of your iPhone, iPad, and iPod touch - https://support.apple.com/HT204215
Change backup files location (OSX and windows) - https://discussions.apple.com/thread/6464086
https://discussions.apple.com/docs/DOC-7392 - see box at bottom on how to do this in Windows
http://www.imore.com/how-move-your-iphone-and-ipad-backups-external-drive
http://support.digidna.net/hc/en-us/articles/203504123-Storing-your-iPhone-Backu ps-on-an-Alternate-Location - using symbolic links - "Mac OS X