I would recommend a multipronged approach, actually. You are correct that muscle burns more than fat, and that is where I would start. Take a look at a good weightlifting program such as Stronglifts 5x5, which will give you an excellent muscle building base. As you build the muscle, you'll contribute to fat loss as it will require more calories on a daily basis to maintain.
As far as the dietary approaches go, you are correct that eating less will help, but you also need to look at what you are eating. It does no good to put the time in at the gym, if all you are going to do for your diet is go from 2 Big Macs at lunch to 1. I would slowly shift your eating to a more healthy structure. You will want somewhere between 1-2 grams of protein per kilogram of body weight per day. (Kilograms is pounds/2.2, 176 lbs is 80kg). I say slowly, as suddenly switching your entire diet is likely to create cravings that undermine your efforts and promote binge/splurge eating.
As part of this, add small salads and healthy soups to your main meals, and eat them before the main meal. This will help curb appetite, and suppress the urge to overeat. Also, eat a bit slower. The "I'm full" feeling is controlled by stretch receptors on the stomach walls, and the signal can take a few minutes to get to the brain. If you are shoveling in food as fast as you can, this can lead to overeating. I wouldn't worry too much about following this diet or that diet, but aim to get around 20% of your calories from healthy fats, another 30-40% from lean proteins, and the rest from healthy carbohydrates (The less refined the carb, the better.)
Start a food log. Learn to weigh your foods, and accurately count calories. Aim for 1-2 lbs of loss per week. In the beginning you will probably lose a little faster, later it will be harder. Don't be discouraged, it will eventually come off. If you need to, find support channels (Such as exercise groups, friends, here), as going it alone can sometimes get discouraging.
I would also add cardio. You don't have to go to the gym, and at the beginning, it can be as simple as a 10 minute walk. This will also help with caloric burn and metabolic increase, and is easy to do every day.
You will have ups and downs, there will be days when you will cheat (Which is perfectly find), but if you stay with it, eventually the weight will come off, and all along the way you will be getting healthier and more fit.
And finally, it sounds like you have been somewhat heavy most of your life, so as a precaution I would schedule a visit with your family doctor. Weightlifting and various cardio exercises can cause quite a spike in blood pressure and heart rate, make sure you're healthy enough to do what you intend to start.