In Germany you could do a "Nebengewerbe or Einzelunternehmen", where you can write invoices in your name, this is a fast way to get started.
Otherwise you have the UG, which can be created with 1 EUR "Stammkapital", or the GmbH with 25k EUR, but you only need to have 12,5k when founding it.
Which taxes have to be paid is different if you do the "Einzelunternehmen" or found a company (UG/GmbH). With the company there is the Körperschaftssteuer instead of the Einkommenssteuer, additionally the regular Umsatzsteuer (19%) and also you have to pay Gewerbesteuer. Gewerbesteuer, Körperschaftssteuer and Einkommensteuer all have a free amount per year, if you don't hit that limit you don't have to pay it.
I would advise against founding in a different country, because taxes have to be paid in Germany and founding a company outside of Germany makes it a mess and really expensive.