If you are using the weight machines there is no need to adjust for proper form. The machine sort of enforces it.
You require proper form for barbells so you do not hurt yourself. You will also get more bang for the buck with barbells because you must use your stabilizing muscles in your torso and back to control the movement of the weight. If you decide to use barbells, you definitely should reduce the weights and find a good starting point. But don't just go randomly to 30% reduction. Find a starting place that is challenging to you but not impossible. Gradually put more weight on the bar each session.
Lots of people in their 60s and even 70s are doing the Starting Strength program. It's worth a read so you better understand the theory of strength training.
Female, 5'3", 48, Starting weight: 163lbs. Current weight: 135.
Starting squat: 45lbs. Current squat: 145 x 4.