for New rules of lifting, I'd go with dumbbells (various sizes), a ball, a step, a bench (although you could probably use the ball for some of the bench exercises) and possibly a barbell.

I bought a barbell to do some of the barbell exercises and was a bit amazed how different they were with a barbell than a dumbbell. The step is useful for doing incline pushups and step ups although I've been using my stairs for the incline pushups. I don't know what is beyond my current level (level 1 of 7) but flipping through the exercises, that seems to be the general equipment.

I have my first personal training appointment next week, and I would be happy to share any advice I get, if you are interested.