I think it's pretty cool that StrongLifts and Starting Strength have been brought up here. Hopefully you are still with us, cozycataloger, because this is some really good stuff.
Learning to lift properly with a barbell, and doing a basic program with those barbell exercises will get you vastly better results than just randomly hitting machines. You're already on the right track, Cozy, moving to the free weights, and doing squats.
If you really want to get the most bang for your buck at the gym in terms of strength training I would recommend reading Mark Rippetoe's Starting Strength
(link WFS). It is the best breakdown of the major barbell lifts--squats, deadlift, press, and bench press--on paper. And a program with just those lifts, and perhaps additional ab and lat pulldown work for you, will get you stronger a lot faster and with less time in the gym than the stuff the vast majority of people in generic gyms spend their time on.
So, good luck, ignore the stupid trainer at the gym, and keep us posted on how things go!