How to properly construct objects on ATmega2056?
I tried working constructing in the global scope, but I get garbage values printed to serial ...


Constructors in global scope are called before init and setup and thus are probably executing too soon for you. This would account for the garbage printed to serial, because your constructor is printing before the Serial.begin() call.

You can put constructors in global scope, however they should do fairly trivial things (eg. setting a counter to zero, or a pointer to NULL). Do not rely upon the system being initialized, thus do not call functions like millis, nor should you be using dynamic memory allocation at this point.

Most classes defer their "real" initialization to a begin function (eg. Serial.begin) because it is safe to do that, usually in the setup function.