That’s great. Totally agree, you should take this step while you are young and will have much more job opportunities.
Just so I don’t mislead you, the 1500-2500 is based on my personal experience being over the age of 21. In your age bracket 500-1200 is more realistic.
Then your accommodation costs will range from 350 (if you are really lucky) - 1200. You might spend most of your money on accommodation and then you need at least another 1000 each month for living costs.
Might want to wait until you are 21 so you can get full minimum wage.
Do you have the birth certificate of your great grandfather? Do you have the birth certificate of your grand mother? Was your grandmother born in Germany?
As far as I know citizen does not pass through the mothers side.