Of course native solutions is always your first choice, but there's always but. iCloud is not really reliable, and the data storage (5GB free) is quite limited.
I've been struggling with this task as well, trying plenty of options. Btw including Dropbox, which is good for storing, but unbearable when viewing. Google Photos is nice for both, but I don't like it organising the images into categories for me and limitations in the way library displayed.
I'm planning to try flickr in the near time, when I'm ready to plunge into piles of miscellaneous images across all my devices. It looks like they can help me do the thing.