The standard weight is 78kg, which is a little too much for you, but a man, this height and weight are quite good. Usually, a healthy weight should exceed a little, otherwise it belongs to emaciation.
You made the right choice. Go to the gym!
Regarding fat reduction, I understand that you want to reduce fat in some parts, but there is no such thing as local fat reduction.
So you need to do aerobic training seriously, 3-4 times a week, either near home or with the gym. 30 minutes at a time.
To lose fat, you must practice strength. The plan is similar:
Day 1: Chest+Brachial III+Abdominal muscles;
The second day: back+biceps brachii+abdominal muscles;
Day 3: legs+shoulders+abdominal muscles;
Most of the people who practiced very hard also started from this plan. You will become strong, too.
Here, I only talked about the plan, but you should actually know the action. However, you should know that Baidu knows that it is difficult to put pictures, and there are so many training moves.
Then, the best way is to buy magazines and read forums (such as Baidu Fitness Post Bar), which are illustrated with pictures and texts, and standardized actions are better.
Although you are not fat, it is a good habit to keep a regular and quantitative diet.