Where in the body you will lose weight first depends on your genes. Your focus might be to lose your belly fat first, but this is not in your control. Human is a complicated creature, so it cannot be clearly said where you lose or gain weight. But in most of the cases, the first place you put on the fat is generally the last place it comes off from. If your arms have gained fat recently, then you lose that fat first from there once you start exercising and following a healthy diet. If you have a pear-shaped body frame than you might just get smaller in size, but will retain the same frame of the body. But remember the fat cells do not disappear, if you will increase your calorie intake you will again gain weight.
Mostly, losing weight is an internal process. You will first lose hard fat that surrounds your organs like liver, kidneys and then you will start to lose soft fat like waistline and thigh fat. The fat loss from around the organs makes you leaner and stronger.