Look into Stronglifts 5x5 - it's a very simple program. I think it was vital to regulating my hormones and helping me to get pregnant. You can Google it or there is a great group on MFP called Stronglifts for Women. The program is heavily geared toward men as far as the write ups but lots of women do it - the group is nice because it's always all women.

I started strength training in January and I love it. I would suggest starting with the machines though, that's generally what they're there for, people who are just starting out or people who for whatever reason aren't using freeweights. Just use the machines for a couple of weeks to get yourself into it, then start moving to freeweights. I only started moving into using the free weights a couple of weeks ago and I wish I did it sooner cause I'm feeling much more from it than on the machines - though I do still use a couple of them on leg day, namely the leg press and the leg curl etc, but I do squats as well.

You might put on a bit of weight at first but don't worry. I've put on weight again in the last six months and I've still lost inches. That might be a better way of measuring progress than using the scale because at first your muscles will be sore and retain water to heal, that'll probably happen every time you work them, but eventually you'll start to gain muscle and you'll see a higher number on the scale perhaps but still be a few inches off. Gaining muscle is slightly easier for us with PCOS than women who don't because of the elevated levels of testosterone, but only slightly. So you likely won't bulk up or anything but you'll find it slightly easier to tone up

I second the Stronglifts program. I know more about weights, so I read the New Rules of Lifting for Women book and followed their routine when I got back into the gym after my baby. Now I create my own programs and change them every 6-weeks. When I was first starting out, I invested in a personal trainer for a short amount of time. It's really worth it to have someone help you check your form and help you get a good routine put together. It's very helpful to have someone who is familiar with the equipment and knowledgeable with lifting to give you a hand at first.

This is a little bit older pic, but here's a progress shot of my back since starting heavy lifting. This is roughly 2-years. I swear by it!