I work out Mon-Fri 30 minutes on the treadmill. Get your heart rate up then get it back down. I toggle between 3 and 5 on the treadmill. Also, I do the weight machines for 30 minutes daily (arms on mon and wed, shoulders/back and legs tue and thurs, abs on friday).

HIIT style workouts are found to be the most effective for PCOS right now according to medical journal. They have a variety of benefits for our bodies and another great thing is that they are a shorter time period. Medical research has proven that a proper 20 minute HIIT workout can be just as effective as an hour of cardio. I don't know about you, but my time is valuable and although the HIIT workouts push you hard, they are much more worth it to me.
Next, focus on resistance training workouts. Muscle burns more calories than fat. Having more muscle allows your body to burn more calories even in a rested state. This is why it helps women with PCOS to have more muscle. Those two styles are the best out there right now according to the research,

CONSULT YOUR DOCTOR first though. I do not know your fitness level, your experiences with working out, or your body. You do. Use your best judgment with trying new workouts.

Body weight exercise are great also. Lunges, push-ups, jumping jacks, planks, squats, wall squats, stretching...I do a bit in the mornings, to get me started for the day. I even have hand weights in my bedroom.

Just starting to move more is great - don’t underestimate the power of walking! But if you want to be in the gym and aren’t sure what you’re doing there are various options. Try some of the classes and see what you enjoy (if you don’t enjoy it you’re less likely to commit). Also, find out if any of the personal trainers offer a free taster session... i’m a PT and will always offer this. You might decide to do regular sessions or even just once a month to get a new program to follow (I have loads of clients who do this to keep their interest and make progress). Hope this helps!

HIIT workouts are great. But the one that has worked for me the most is heavy weight training. It needs to be heavy though - struggling or failing to get the last few reps out. I do a sort of body building workout so leg day, chest day, back day and shoulder day plus a couple of HIIT sessions a week. Heavy weighy training really improves hormone imbalances and regulates insulin and its fun too!