Over LAN with flavored solution of your choice.
Other than that, I use one of my spare drives and my USB docking station if I need to move it outside of my own house. I never really had a need for dedicated external drives but a docking station is handy for many things, this being one of them.

Archivebox might be something to look at. Open source, self hosted, made for archiving websites.
So it not only keeps track of your mass of links, you can also snapshot/archive them when you add them. So if they ever were to go down, you’d still have a copy yourself.
https://archivebox.io/

Though to be fair, I have not actually tried it out myself. I looked at it a few times but I don’t personally have a need for it so. Worth taking a look at though.