For those who care and have similar questions - the results of my encounter with experts accountants and lawyers
As I reminder I live in Hungary, therefore statuses are those of the local legislation, but equivalent do exist at least in most of Europe. Not sure about US/Asia
The status that works best for my case (see initial post, "amateur/hobbyist" without an infrastructure) is "self-employed" (exact term "önálló tevékenységet végző magánszemély", e.g. "individual working for himself", sort of) ; this is roughly similar to "independent", "sole trader" and/or "micro enterprise" depending on the country.
I only need to register with the Chamber of Commerce to obtain a "business tax ID" ; this is all done WITHOUT incorporating. Invoices, if any, are therefore done with the name of the person, not a company.
For information purposes, here this costed me ~50€ (25€ administration fee + 25€ as I preferred to have the paperwork done by the accountants as it's all in Hungarian, which I don't speak)
Without an actual company, constrains are minimal (no business bank account, no payroll, no minimal regular social contributions, etc.) and we are only taxed on benefits (revenue - spendings ; income tax + contribution + vat + etc.)
Sounds simple enough in principle ! I'll know more about the actual details when I'll go through some figures.