I'd back them up anyway, just in case.
If you have a Kindle (just for example) you will still be able to read your books if your device breaks. You just get a new Kindle and register it to your account.
Your family will be able to read the books you purchase, their readers just have to be tied to the same account.
If the books have DRM, you will only be able to read them on that company's reader. If you have a Kindle, you won't be able to read books that have B&N's DRM, and vice versa.
On the other hand, books that don't have DRM can be read on any device. PD books from Project Gutenberg and other sources do not have DRM, and there are sellers that don't use DRM.
I haven't had to use Amazon's customer service, but I've heard it is good. I really haven't looked into customer service. A friend of mine had a bad experience with B&N's customer service, but that was a couple years ago, I don't know what it is like now.