I use Carbonite as my cloud backup. You tell Carbonite to copy the desired files, it does the rest.
In general, you want your backups to have the exact same folder structure and file names as your originals. This implies that after you import the photos into Lightroom and if desired some initial renaming, that you leave the originals in that exact same folder structure and have the same file names as well.
You should allow the built-in Lightroom backup to run on a periodic basis (every day or every week). You should check the box to have the backup check the integrity of the catalog. You should then have your cloud backups service copy these backup catalogs made by Lightroom.
can anyone recommend a good one to access photos from the cloud on my iPhone 6S and/or iPad Air2
Well, there's the Lightroom Creative Cloud service (called Lightroom Mobile) but this is NOT a backup. It does let you view the edited photo, however.
The problem with other Cloud backup services is that when you access the photo from your iPhone or iPad, you will be only able to see the unedited version of the photo, is that what you want?
As well as keeping all my files on external drives, my choice of Cloud Back Up was Adobe Revel, synced across desktop and mobile apps and was great for viewing and sharing (and once had a LR plugin).
Anyway, Adobe unfortunately decided to close the service last month but my reason for posting is that, in the closure documentation, it was said that Full Resolution Cloud Storage would be coming to Lighroom at some point (Lightroom Web and Mobile have a similar interface to Revel so it wouldn't be a surprise).
As dj paige has previously said, it hasn't been announced yet, but I thought it's worth letting you know to keep an eye out.
To a new LR user like me, it seems the next logical step in the development, especially making the whole workflow smoother across all platforms.