Salvaging a rootless paph

[andrew__]

I was given a Paph. a while ago by someone who had given up on it - "save it or toss it" were the basic instructions.

Here's what I'm working with:





It looks like it had flowered and a new fan of leaves started to grow, and then it grew, and continued to grow until it reached where it is now.

Now to me in my uneducated ways those things along the stem appear to be some sort of root node things, maybe, and some of them seem to be newer and greener than others which seem older and blacker. Will it root from these "nodes"?

What would you do with this thing if it were your orchid?

Ultimately I'd like this plant in S/H culture - should I be rooting in water culture, sphag & bag or just stick it in hydroton in a pot and stick that in my mini-greenhouse?