how do I efficiently move large files to external drive to clean out hard drive space?

I have intel iMac, I take lots of photos and video of grandchildren and as a result hard drive (250) is full. I have external hard drive that I've tried to copy photo library to but as there are so many it's hard to verify they're all there (on external drive) before I delete from the hard drive. Is there an efficient way to move them and other things to an external drive like a program. Also if Carbonite only backs up the hard drive, how do you back up an external drive?