The rule of thumb for backups is having a 3-2-1 plan

3 copies of your data (including the original, ie. iPhone, iPad, and Mac)

2 different types of media (external hard drive / cloud)

1 of the backups should be in the cloud

I do not recommend that anyone signs up for iCloud Photo Library. it’s giving people fits. There are other options for cloud photo backup directly from the iOS device..

Google Photos is an option. They will give unlimited storage for free, but not everyone likes Google.
One Drive from Microsoft (15 GB for free and more for a small fee)
Carbonite
Dropbox

I can discuss these more in depth at a later time.

San Disk makes a USB flash drive that you can connect to the iPhone or iPad. It is for intermediate transfer between phone and computer.
http://www.sandisk.com/products/mobile-flash-drives/ixpand/

* You can also free up space on your iPhone by importing them into Photos (formerly iPhoto) on your Mac and choosing the “delete from iPhone” option on import. The same can be done with Windows Photo Gallery or another photo management program in Windows.