There's no one "right" way to stay fit, and that includes lifting weights. There are different weights to lift (barbells, dumbbells, kettlebells, etc.), machines and free weights (and hybrids), different sets/reps schemes, tempos (time it takes to raise and lower a weight), rest periods, and many more variables.
Sensei Hutch of Seven Tigers Martial Arts has been training with weights (machines and free weights) for many years. Recently, I had a discussion with him about his weight training methods. His commentary is paraphrased below.