iCloud is doable. iCloud offers 5GB free last I checked, and if the user has a lot of photos and videos, it might be best to customize the iCloud settings to only backup photos and videos and not other things on the phone.
You then make sure stuff is backed up then you can access the iCloud photos and videos via the iCloud website.
as I mentioned though, any photos and videos taken directly with the phone (or carried over from a previous iPhone that were also taken using the camera) will be available by just plugging the phone into USB on the computer and opening it up.
As for a third party method, using the cloud, you can use Google Drive which offers a free 15GB of space and then access the photos and videos via the Google Drive website.
Using a third party method such as Google Drive lets you upload anything, whether it was taken using the phone, or downloaded from social media/text message sharing.
If wanting to get files off the device that are not just in the camera roll using USB, then a third party app that essentially turns your phone into a flash drive is needed, but you'll need to do some basic searching for what's available because I haven't messed with that sort of thing since I had an iPod Touch 4 and 5 and I haven't owned and used any Apple products personally since then (I only ever touch an iPhone when my mom needs me to help her with something, or a Macbook Air for my grandma, otherwise I use Android and Windows)