Tank instructions are usually not very helpful, and neither are most shops.
The stress coat is needed, you should add it straight away. It removes the chlorine or chloramine added by the water company to kill bacteria in the water supply. It will also kill the bacteria you want to grow in the filter and when you have fish it will irritate them too. It should be added when the tank is first set up, then to the new water whenever you do a water change.
Quick start is a bottled bacteria product. Unfortunately it contains the wrong species of one of the two bacteria. There are only two products that contain the right one because the companies that make them have copyrighted the use of the correct bacteria so no-one else can use it.
Shops always ridicule fishless cycling. Either they don't understand it or they are afraid their customers won't understand it. I would strongly recommend you do a fishless cycle; because it is a classroom tank, will you have access to it at weekends and holidays? If you use the quick start you may well find you have to do daily water changes which could be a problem at weekends. You can use the quick start, if it helps it will speed things up. The danger is that you could add the quick start, the shop then does the tests and tells you to get fish, but without fish or ammonia from a bottle, the tests will show good results - until you add the fish. If the quick start has done nothing, you will then find yourself doing a fish-in cycle, which requires daily water changes, sometimes several changes a day if there are a lot of fish.
My advice would be to get a liquid reagent test kit (cheaper on-line) and a bottle of ammonia from the cleaning section at Homebase or from Amazon/Ebay. The follow the instructions in the filtration and cycling section
hereFish - provided you avoid fish that are known to do better if soft alkaline water, you should be OK. Though choosing fish that like hard alkaline water is better. With a cube shaped tank you need to avoid fast swimmers as they need a fair amount of horizontal room to zoom about in.
If you like bright fish, have a look at endlers. If you shop around you should be able to find several different pattern types. But males only. Livebearers like endlers breed worse than rabbits and while it would be educational for the pupils, you'd soon be very overstocked. Besides, the females are plain grey

Another choice would be guppies, again only males, but they are more delicate than endlers.
Golden pencilfish aka beckford's pencilfish would be OK, they do have red in them
Fish of the pseudomugil genus - the most common ones are P gertrudae, P signifer and P furcatus. They would be better in a longer tank but they could be OK in yours. Have a look at the website seriously fish for their profiles.
Scarlet badis (Dario dario) though they can be picky feeders.
Just a few suggestions

aquadvisor has a terrible reputation. Have you looked at the community creator on here? Go to fish profiles, click on any fish and down at the bottom of each profile is the CC. You do have to register then log in separately from the forum to be able to save your info - use your email address not your user name.