You look great in your photo! Awesome that you fit into that dress too!!
A few answers about exercise, I'm a qualified fitness instructor and I would tell anyone, trying to lose weight or not, to do both strength training and cardio. Strength training gives you lean muscle mass and increases your metabolism, improves bone density, improves the strength of your joints, and so many other wonderful things. Cardio is great for strengthening your heart and cardiovascular system, fat burning, improving blood circulation to your limbs, and again many more things.
Really it depends on what you are trying to achieve and what your specific goals are. I would say to anyone to take baby steps when starting a strength training program, even if you have worked out before but just haven't for a while. Strengthening ligaments and tendons is important before trying to lift heavier weights on a regular basis. I'd also say that women SHOULD be lifting heavier weights though- we aren't genetically built to gain mass muscle in the way men are, so no matter how much weight you lift you aren't going to look like Arnie in his prime!
Also when structuring a program for yourself you should focus on main muscle groups, as they are the ones that will burn the most calories doing them and need the most strengthening anyway! So think back, chest, quads (front of thigh), hamstrings (back of thigh) and glutes (butt). I usually don't bother doing arms as well, just because usually with chest and back exercises you are also using your triceps and biceps (ie push ups- chest and tris). A really good core strength exercise is the plank/bridge. It works your TA which is the band of muscle around your stomach, it kind of holds you in. It's the deeper abdominal muscle, whereas crunches will work the superficial muscle on top. You can of course do both
Hope I've been some help, if I've just confused you feel free to message me, haha or just ignore the post!