Also, thanks Matt for your input. Your option is a good one also, but I don't have a NAS currently, so I can't really use it.
No worries! Happy to offer another method. iCloud is probably the better way to go since it's native and you'll be able to do more with it. I like that it'll keep a smaller version on the phone so you'll still have them to show to people. That's the issue we're running into.
I should mention that you don't really need the NAS, since Dropbox runs on any computer. Dropbox also has its own photo management service, though I haven't used it.