I’d highly recommend you consider incorporating weight training in your plan if weight loss/fat 
loss is your primary goal. Weight training burns calories and builds lean muscle mass—two important keys for losing fat.
I’m not discounting the importance of cardiovascular/aerobic training—many people are able to lose weight without ever touching a barbell or dumbbell. But it seems the most effective approach would be to integrate both weight training and cardiovascular training into your routine. Bodybuilders and other fitness professionals have successfully used this approach for decades.
One study, for example, compared two groups of obese teenagers who suffered from metabolic syndrome. One group did only aerobic training (AT), while the other did aerobic training and resistance training (AT+RT). Both groups improved, but those who did aerobic and resistance training showed the greatest overall improvement:
Indeed, the AT+RT group had significantly higher changes throughout the intervention in body composition, total cholesterol, waist circumference, glucose, and adiponectinemia.1
Should you stick with high repetitions if weight loss is your goal? Probably not.
Another study compared the effects of high rep training (15 reps) to lower rep training (8 reps) in fourteen female subjects. The lower rep training had a more significant metabolic impact in terms excess post-exercise oxygen consumption (EPOC). The low-moderate rep range (8-12 reps), therefore, would seem to be the more logical choice.2
Conclusion:
Consider weight training with moderate rep ranges if weight loss is your goal. Combine it with a negative calorie balance and cardiovascular training, and you’ll be well on your way to a leaner physique.
For women I’d highly recommend a program like Bikini Body Workouts.
I’d recommend No Nonsense Muscle Building (2.0) for men who are new to training.
References:
1. J Clin Hypertens (Greenwich). 2011 May;13(5):343-50. doi: 10.1111/j.1751-7176.2010.00388.x. Epub 2010 Nov 8. Long-term effects of aerobic plus resistance training on the metabolic syndrome and adiponectinemia in obese adolescents.
2. Med Sci Sports Exerc. 2002 Apr;34(4):715-22. Effects of resistance exercise bouts of different intensities but equal work on EPOC.
