Is this plan a good one? Weights/Cardio for weight loss

Hi all. Some background. I have PCOS, 28 year old female. Currently at 240 (ouch), wearing size 16/18. Would like to get down to about 150 weight-wise or at least size 6/8 since the scale isn't everything (see! I have learned from lurking! :-) )

I get to the gym about 3 days a week, 4 if I am being an over-achiever. I wear a heart rate monitor which is really helpful to me. I start out doing about 20-30 minutes of cardio, usually elliptical or the stationary bike. The gym I use is limited on equipment, so other than a treadmill, those are my options. After my cardio and getting my heart pumping, I move on to weights.

I have been doing what I think are more compound movements, focusing on multiple muscle groups instead of isolating. So I have really kind of been doing full body strength training every day, some days I will focus more on upper or lower or abs. Here are the workouts I typically do:

3 sets of 10, goblet squats
3 sets of 10 plie squats
3 sets of 10 lunges
3 sets of 10 deadlifts
3 sets of 10 chest flies
3 sets of 10 lateral raises
3 sets of 10 front raises
3 sets of 10 upright rows
3 sets of 10 russian twists
3 sets of 10 (i don't know the name for it, but I hold a dumbell perpindicular to the ground out straight, and twist from side to side)
3 sets of 10 shoulder presses
3 sets of 10 tricep extentions


NOW, I DO NOT DO ALL THESE EVERY DAY! I typicall choose 5-6 each day and do those, trying to balance them out between upper, lower, abs, and so I don't get bored, switching it up. Also, are there other workouts I could add in with these ones?

I know different things work for different people, but from other's knowledge/experience, should I switch to something like NROLFW or Strong Lifts? I am not interested in making big gains, I am interested in increasing how much muscle I have and decreasing how much fat I have and getting smaller. Of course I want to be stronger, and do not want to be "skinny fat" which is why I am not a cardio bunny. Input very greatly appreciated! Thanks in advance :-)