How do i get started? Cardio or Weights first?

So if weightloss is your goal then continue with your calorie deficit.

If you want to improve your cardio health, then start by doing walk/run intervals on a program like Couch 2 5K.

If you would like to strength train to retain your muscle mass as you lose weight and become stronger, then I would suggest a free weight training program such as Starting Strength or StrongLifts 5x5.

You can definitely do both - tons of people do, but you should not let one program interfere with the recovery of another.

At the beginning, it's more important to develop the habit of staying active daily with lower-intensity activities ( walking, cardio, etc), and to increase them gradually to avoid injuries. I would wait a couple months before starting strength training, unless you can work with a good personal trainer. Obese beginners often have muscle imbalances and poor movement skills, which can lead to poor form or overuse injuries. Whenever you're ready, follow a proven strength program, don't do your own thing. If you can't work with a trainer, i suggest New Rules of Lifting for Life. A barbell-based program might not be ideal for starting out.

Exercises don't target fat or loose skin, so that doesn't modify your exercise program. Much of the loose skin may snap back on it's own within 2 years of losing the weight.

Search for the PCOS group. The consensus seems to be that keeping carbs low helps. I mention this because some people's notion of a healthy diet is high in carbs (vegetarian, juice, etc).

I would (and did) master some bodyweight movements before moving on to lifting. As mentioned already, strength work seems to be very beneficial for women with PCOS. In my experience, being more active in general helps immensely. It does for everybody but I can say that being active every day for 45-60 minutes minimum let me lose 50 lbs while averaging at least 1750 calories while other women I know with PCOS who did not make a point to be active every day complained they had to eat 1200-1400 to lose.

Pick an exercise you like- you are more apt to stick with it. Once you get into good gym habits you can start adding stuff in. I loved running but eventually added lifting in, which I loved a lot less but the knew would help me overall with both my weight loss and running goals.

I also second starting weights with a good trainer. You can very easily hurt yourself otherwise.

Your primary goal should be - safety first. Avoid injury. At 139 kg, getting into heavy lifting with barbells and such, it's going to be easy to hurt yourself. Plus you dont need to build any more muscle. You will be able to preserve your muscle with just general exercise. Walk a lot, do low impact exercise like elliptical (with resistance), etc.

Do whatever feels good to start, get some variety in your routine so you have sustainability and open yourself up to more options. You'll end up specializing naturally.