Every person registered in Germany is required to have a health insurance. If you get insured some time after registering, you have to pay retroactively to the day of registration.
There are multiple possibilities to bridge the time between arriving in Germany and moving the official domicile to Germany. In some cases it is possible to remain insured with the parents in a foreign country, as long as the insurance covers the stay. Otherwise it is possible to get a travel insurance, or an insurance for foreign guests. An example of such an insurance is Hanse Merkur Insurance for Foreign Guests, which also covers people with German passports for up to one year. http://www.hansemerkur.de/produkte/reiseversicherung/auslaendische-gaeste/jahresversicherung
In Germany you can choose between statuatory and private health insurance. You can only insure yourself privately, as a government official, when self employed, or with a yearly income over 54’900 Euros, meaning most students get a statuatory health insurance. The two types differentiate in covered services and when calculating rates. A private insurer has a constant rate, while the rate of the statuatory insurance varies on income.
It is important to get a liability insurance. It regulates damages done by you to others (property damage, personal injury).