What kind of system (dimension of tanks, water quantity,beds grow, number of plants and fishes) I should have for satisfying a family (3 or 4 persons maximum) for a whole year?
And what do you think about vertical beds grow, as that ones used in Hidroponic? Is it possible? Is it a good solutions for little spaces?
First you will have to define what you mean by "satisfy" Are you asking for a system design to provide 100% of all the food/calories per year for a family of 4? Or will you still be buying bread, oil, sugar, coffee, beans and fruit from outside the system?
Does satisfy mean you need to get 4 fish out of the system per day/week? Or are you happy with just occasional fish?
What kinds of fruits and veggies your family eats will play a big role in what you should grow and the design of the system. Dietary tendencies will vary greatly and many Americans being poor at eating their veggies means that many people here are still learning what to grow and how much as well as when to grow it.
So I would advise to get started with a modest system to learn and what you learn from that will help you build the bigger system to take care of more of the family's needs. Aquaponics is addicting anyway so planning on expanding later.
There are vertical methods of growing but keep in mind that when you start stacking or going vertical you will be reducing the amount of light getting to the lower levels so planning needs to be done carefully to keep things productive. Most vertical methods are appropriate to small plants and when you have to pump water higher it takes more electricity to do it.