Aha! Well, that's more modern than the one I was thinking of, but the same basic design. (It looks like it lacks the funny focusing track mechanism I described as something you might want to lock down. It's just as well, I think: I never thought that mechanism was really precise enough to justify itself. Same basic design, otherwise, though, : perhaps not quite so heavily-built, it'd appear. Which should help you move it.
You can see the little screw I described to remove the lamp bell: (like you would to change the bulb: this might help to move things. As well as get the wire out of the way.) At least make sure it's locked down. Sometimes people'll just sit them up there ...without noticing, if the enlarger hasn't been moved in a while.
I'd probably definitely want to load the enlarger first. And, well, probably take a bunch of the offered stuff: for the most part, no one thing is terribly expensive, but it adds up to gather everything from scratch.