Updated: Apr 8, 2019
The best exercise you can do for fat loss is anyone you choose to do in a calorie/energy deficit.
Yes that's right this is actually a post on nutrition not exercise. The truth is there is no one exercise that is better then another when it comes to losing weight. Yes, while obviously an exercise like the squat will work more muscles, build more strength(which should always be a focus), and burn more calories then say bicep curls. While movement is still a huge component to weight loss, it doesn't really matter what exercises you are doing in the gym until you adjust your nutrition accordingly.
The key is being in a calorie/energy deficit. All this means is that you are taking in less calories then you are burning. This is most easily achieved by reducing the amount of food you consume, increasing your energy output(exercise), or both. To do this you need to be able to find out how many calories you burn daily. A simple formula you can is taking your bodyweight and multiplying it by 12. That will give you a rough estimate of the amount of calories you can consume and still safely lose weight. This number is just a jumping off point though, it is not exact. It doesn't factor in lean body mass or your activity through the day. If you are losing weight to rapidly then a bit more and if you are gaining a bit less. The best way to find out how much you should be eating is to track you macro(and certain extent micro)nutrients: protein, fats, and carbs.
This means you will have to keep track of the food you are eating, Myfitnesspal is a popular food logging app. There are many to choose from though, so pick whatever is easiest for you to use. Once you have chosen your method of tracking start by taking weekly averages of your daily calorie intake as well as your weight. Look at your calories and your weight, if your weight is staying still or raising then that's a sign you need to reduce your calories and/or increase your energy output a.k.a. move more. Don't be to worried about how much carbs, fats, and proteins you are consuming just make sure your are staying in a slight calorie deficit, usually about 100-250 calories below whatever your maintenance calories are(the amount of calories you can consume that keeps your weight at a constant number).
While the quality of food is important, when just beginning your weight loss journey it is best to focus on reducing calories first. Then start focus on eating whole, nutrient dense foods. Once you get a good understanding of how much calories you are consuming you can stop tracking and start to learn to eat intuitively and still stay on track while still eating foods you enjoy.
Though it can be a bit more complicated then what I've laid out here, this is still a great place to start. So remember if you want to lose weight, worry less about what you're doing in the gym and worry more about what you're putting in your body outside of it.
I hope this information can be helpful and good luck on your weight loss journey