First off, it sounds like you have made some good progress. You're going to be shocked at how fast you can lose fat when you add in a good weight training program. Lifting weights will burn far more than cardio will, and as you build muscle, your caloric demands will go up, making your body better at burnig fat. Instead of just focusing on gainig muscle or losing fat, I dont see any reason that you can't focus on both. Diet is going to be the key to making your new program work. Controling carbs while eating whole food sources, rich in protein as well as healthy fats will help you build muscle while keeping your insulin low. Focus on animal sources of protein like boneless skiness chicken breast, lean beef, omega eggs and egg whites and fish. These should be the foudation to your diet. If you have never trained with weights before, it might not hurt to hire a good trainer, who can help set you up on a program. After a couple wks, you should be good to go off on your own. On this program remember than muscle weighs a lot more than fat. You may not see as much movement on the scale. This is ok. Use the mirror and use progress pics to watch your progress. 

Once you get down to about 12% BF, I would probably try to begin adding more carbs back in, to focus less on fat loss and more of lean muscle growth. Just be very careful. It sounds like you store fat very easily, so "bulking" could get out of hand quickly.