The first one isn't what you think it is. It is, AFAIK, only for complaints against EU institutions. For everything else (national, local, private and non profit entities) you need to contact the relevant national data protection authority
You only need to know who your own regulator is for the country you live in. You file complaints to your regulator, and they collaborate with the regulator for the country where the company is established. This is called the "One-Stop Shop Mechanism" for GDPR: both consumers and companies only have one regulator to contact.
There is also an online dispute resolution center: https://ec.europa.eu/consumers/odr/
This allows you to complain about a European company if you deal with it from another EU country.