There is no need to do cardio if you'd rather be lifting weights. Just make sure that you're lifting heavy and getting your heart rate up while you work!
(I do agree with Resolute that you could be merrily losing on way more than 1500 calories. Honestly, I'd start with 2200 or something and see how you go. You're going to be at this for a long time--there's not much to be gained by starting out with such comparatively low calories.)
Re the weight lifting. There are many, many ways of doing strength training. You can do full body every other day. You could alternate upper and lower body. You could do a bunch of splits with lower, chest, back, core. You can do many reps in 2 or 3 sets or few reps in 3 or 4 sets. You can do long rests or short rests, supersets or just straight up sets. The possibilities are endless.
If you're happy with what you're doing, keep doing it for now. If you want to push a little harder, I say find a program to do. I personally love the New Rules of Lifting--both the 'man' version and the woman version. They are comprehensive plans that tell you exactly what to do every day. There are other programs but I haven't tried them yet.
But basically, don't worry so much about having a perfect plan and really put your energies into developing your form. Work on doing excellent deep squats, solid deadlifts, quality crunches and so on.