Update section for 7 day ticket
Home printed tickets valid for 7 days for central Hamburg are priced at 16,90€ upwards, no HVV card or photo is needed, just bring a passport containing a photo of yourself: info, buy them here. They are called weekly tickets but you can freely choose the starting day.
The 1 zone ticket is not suitable as that zone has to be outside of the "Großbereich Hamburg": zone map. Insert the zones you want to travel through (eg. "000" for central Hamburg, containing the Dammtor and main train station), the start date and your name. Payment is possible via credit card (master card, visa or american express) or direct debit (you have to create an account, only German bank accounts supported).