Should the new tires put on in front or on the back?

You put them wherever they are needed. If the threads are bare then they need replacing by law. See a car professional.

If possible, put the best tires at the back. When braking(hard), the weight at the rear of the car will be momentarily reduced, making it easier for those wheels to break free and skid. By having the tires with the best grip at the rear you reduce that risk a little.