A very safe way is building a web extension for your browser that facilitates downloading any media assets that your browser comes across. You're writing the code, so the plugin would be harmless.
It would work like an adblock (it's a plugin that does something on the pages you're surfing to), and it would list all the videos and GIFs etc that the browser has loaded from the page, ideally letting you click to download each very easily.
It needs intermediate to advanced level coding skills.
I'm sure there are already some extensions that you could use as a base, for example this Chrome extension on github that I found now:
https://github.com/rtcoder/Media-downloaderBut that was created by someone else, so to fit your "safest" criterium you'd have to go through the code files and check that it's not malicious (since it's in the Chrome extensions store it's likely absolutely safe).
