Evan,
Just like every thing else about our bodies and medicine there is no simple answer that fits all. I'm sure you've already figured that out from the variety of answers you've gotten here. Allow me to add to the variety. I'm pretty much of the same opinion others have expressed that carbs are the real problem, more so than fat. Here are some random thoughts I have learned through the years.
How fast the carbs you consume get converted into blood sugar is important. That's the glycemic index.
A doctor told me years ago a big problem with our bodies is that when there is excess fat to be stored our bodies generate fat cells to do the storing. Dieting (meaning eating right and sufficiently only) will cause the body to withdraw fat from the cells, but the empty cells remain. Once created they stay, and refilling is easy. That's one reason why people who lose weight find it so easy to regain it.
Our bodies are less efficient at converting fat into energy than converting protein into energy. That's why crash diets harm people. They lose muscle tissue before they lose fat.
Our bodies want to be a certain weight and have a certain cholesterol level. Forcing it to be otherwise is an exercise in futility. But knowing what those "want to be" numbers are is quite difficult, if not almost impossible, to figure out.
High blood glucose levels cause high insulin production, which leads to eventual beta cell burn out. High levels of insulin can act as a poison to the body. One reason to keep your weight down is to avoid the complications of diabetes, but it's not a guarantee you won't still have diabetes. Contrary to conventional thinking, I believe that the root cause of excess weight gain is also the root cause of diabetes. I don't buy 100% the argument that being overweight is the cause of diabetes.
Another reason for high insulin levels is what is called "insulin resistance." Insulin is the catalyst that helps muscle cells convert blood sugar into energy. As cells become more resistant to absorbing glucose the body cranks up the level of insulin to force more glucose into the cells. But high insulin levels also cause more carbs to converted into stored fat. Low conversion levels means low energy levels. It's all a viscous circle.
In order to lose weight you have to burn more calories than what you take in. But like I said, converting fat is harder than converting muscle, so you have to do it slowly and deliberately. That's why exercise is so important. It's forces the body to burn energy but also to preserve muscle tissue. Not everyone agrees with this argument.
My approach to losing weight is to try for high protein and low carbohydrate consumption, and let fats pretty much fall where they may. Is it working? Not sure. I'm getting back to the treadmill to burn up some calories, but it's tough.
Here are some references to research.
Check out the Sugar Busters book and website.
http://www.sugarbusters.com/ The book gives a good explanation of the relationship between carb intake and insulin levels and how carbs get converted to stored fat. I don't buy everything they preach, but it's well worthwhile reading.
Check out the Glycemic Index website.
http://www.glycemicindex.com/ They list several books. Be aware many in the medical community scoff at the value of GI, but again, it is well worthwhile learning about it.
Check out all the other diet suggestions already given. No one of them is best for everyone, but one very well may be best for you. Keep in mind, losing weight is a long term process, meaning 6 months to years. You may have to spend up to 2 or 3 years finding what works best for you. DO NOT expect to drop 50 pounds in the next 2 months. I'm not saying it can't be done, but it won't be good for your body. From everything I've read and experienced 5 pounds a month loss is on the high side of a realistic weight loss program.
Now, here's a couple of items that pretty much go contrary to everything above, and are what my doctor says he is going to follow and said everyone should follow. A fellow doctor has lost a lot of weight following the principles in the following approaches.
The China Study by T. Colin Campbell and
Prevent and Reverse Heart Disease by Caldwell B. Esselstyn, Jr., M.D. Both of these guys argue that if the food product comes from a biological being that has a face or a mother, don't eat it. I'm exceedingly skeptical, but apparently it works for some people. You owe it to yourself to at least check out this approach.
I hope this rambling helps you some. Remember, like I said at the start,
There Ain't No Easy Answers, so don't waste your time looking for one.