Welcome to TFF, and to the hobby.
There are very, very few chemicals needed. If you are dealing with municipal tap water, it will have chlorine or chloramine in it and you do need a good conditioner to detoxify whichever they use. All water going into the aquarium once it is cycled with fish in it must be treated to remove these substances. Before someone mentions it, you can remove chlorine by briskly agitating the water or letting it sit 24 hours--but this is only effective on chlorine, and it does mean containers for the water outside of the aquarium at every water change. Chloramine must have one of the conditioners to deal with it.
If you have live plants, you may need a fertilizer, or may not, depending. That's another big topic.
These two additives are the
only ones you should be adding generally speaking. If you have a problem such as a fish disease, etc, you may need a specific medicine, treatment, etc. But that is a specific emergency-type issue.
You mention Fritz Zyme 7. This is a so-called bacterial supplement. According to the company's website, this substance removes ammonia and nitrite in new tanks. It may or may not help in establishing the nitrifying bacteria. It most assuredly is not going to do any sort of instant cycling on its own. There are several similar products on the market, and they are much the same--they may or may not help, but that is as far as they go. The only two exceptions are Tetra;s SafeStart and Dr. Tim's One and Only. I won't get into all the details, just want to be clear that aside from these two, you are not really getting much if anything.
It is recommended by some that you keep some Aquarium Salt on hand. In 30 years I used this twice. There are a few specific issues where it is a good treatment. I won't go into all that either. The point is, fish live in clean water, not chemical soups.