Way to go on planning to do fishless cycling before adding the fish. It is an important step toward becoming a responsible and successful fish keeper.
If you plan to use Tetra SafeStart, there is no need to transfer the filter media or the gravel from the old tank. The basic idea is to have bacteria seeding to jump start your cycling. Tetra SafeStart already serves this purpose. So there is no need to do them both.
The key is to have everything set up and running. What filter system do you plan to use for the new 25 gallon tank?
It is very important to have a sufficient filter. You may add Tetra SafeStart after the tank is running.
Make sure you do not overdose ammonia. What source of ammonia do you plan to use?
The aquarium nitrogen cycle is not completed until you always get 0ppm on both ammonia and nitrite readings, with an increasing nitrate concentration. <---- Important: It is under the condition that you have a constant source of ammonia. ex: You dose ammonia daily, and at the end of the day you get the readings of what I said earlier.
All those schooling fish require minimal 5~6 to be a school. Less fish in each group will make them feel unsafe and thus behaving unnaturally.
As long as you can complete the cycling with 5~6ppm ammonia dosed daily with a sufficient filter system, you should be safe to add full stock of fish at once afterward. This is one of the good points of doing fishless cycling. It gives you that option of adding more fish instead of a few at a time.
It is an important step toward becoming a responsible and successful fish keeper. 
