I figured the first rank in the leadership perk would allow me to move resources between settlements without having to select each piece and carry it as inventory... but it doesn't. What exactly does it mean when it says you can set up supply lines?

(I had to look this up too.) You need to assign a spare settler to go and set up the supply line between two settlements before it works. While in the settlement management mode if you walk up to a character like you're going to assign them to a function you should see a few options down at the bottom (sorry, can't remember specifically which button it is.) But then you can send that guy to your other settlement and it'll set up a supply line between the two.

Awesome, thank you.

Working assumption: settlements should be daisy chained. You only ever connect to one other settlement in the chain. Unknown: how do you break the chain to reorder it.

For me personally I am only concentrating on 3 settlements for now. I will setup the others, but not really worried about them.

Abernathy farms

Sanctuary

Red Rocket. those are all in the same general area and are easier to maintain.