as mentioned above, calorie reduction is the way to go and any weight loss diet is going to restrict your calorie intake one way or another, whether it is through eliminating fat, carbs, whole food groups, etc. You can lose weight either way you do it, but why not eat a variety of foods to get your nutrients and just watch the total calorie intake from all of it? At least that is my take.
So, calorie restriction would be best. I'd calculate your Basal Metabolic Rate (calculator is found on this site) and your maintenance level of calories (Harris Benedict Equation can also be found on this site to calculate your maintenance level) so you can find your window of calories that you should plan to stay within.
Yes, it is true that your body needs calories to perform exercise, but you will do just fine performing regular exercises on a moderate caloric deficit. Intense exercise would require more calorie intake and an intense caloric restriction would drastically reduce your energy level to perform well. So aim for a moderate caloric intake (somewhere between your BMR and your maintenance calorie level- closer to your BMR though, a caloric restriction of somewhere between 500-1000 calories a day) while adding exercise to your routine to lose weight safely. At the end of the day, it is a caloric deficit (whether between diet, exercise, or both) that will get your your results.
Good luck!