advice before I meet with a personal trainer

[Wynton]

I've used New York Sports Clubs for a while, mostly for their elliptical machines and some of their nautilus machines (which they label their Xpress line (meant for beginners). Because I recognize that the Xpress line machines aren't optimal, I scheduled a session with a trainer to show me the proper way to use free weights and suggest a lifting program. I am essentially a free weight newbie.

When I spoke to this guy briefly on the phone, he asked if I would be willing to try other machines they have, as a transition to free weights. I said sure, I'll try whatever he recommends, but now I wonder whether I should just go straight to free weights.

I can't find pictures of the machines, but the website here describes them as follows:

Secondary - less stable
pin-selected weight or plate-loaded weight
independent movement
unilateral converging
cables stable base
cables unstable base

All of this is supposedly distinct from the "primary" or more stable machines I have been using.

So my questions are:

(1) Should I insist on learning free weights first, or are these machines a reasonable transition?
(2) Regardless of the equipment I use, what exercises and movements should I make sure to learn?
(3) Anything else I should ask this guy?

Keep in mind that I assume that this guy has little advanced expertise, though perhaps I'm wrong about that. He didn't sound very impressive when we spoke briefly over the phone. I figure that so long as I learn the proper motions, I can always return here for advice (or links) about the actual routines I should use.