Here are some basics about the German banking system:

With have four major types of banks
Sparkasse (similiar to mutual savings banks) Largest bank group in Germany
Volksbank (Similiar to credit unions) also very large
Private Banks (With large banks like Deutsche Bank/Postbank andCommerzbank)
Direkt Banken (Banks with have no real brick offices and are only reachable via phone and internet)

Sparkassen have a Germany-wide free ATM use
Volksbanken also allow free use of their ATMs Germany wide
The large private banks have an ATM network called "cash group"

the websites for Berlin are:
Berliner Sparkasse https://www.berliner-sparkasse.de
Berliner Volksbank http://www.berliner-volksbank.de/
The private banks have german wide websites:
Deutsche Bank https://www.deutsche-bank.de/index.htm
Commerzbank https://www.commerzbank.de/
Postbank http://www.postbank.de/

Normally Sparkasse, Volksbank and Postbank have the largest office and atm networks and are focused on private customers. Normally the offer for students free of charge checking accounts (in German they are called Giro-konto)

So your daughter should check out Sparkasse, Volksbank and Postbank.

About wiring money. Check out what the fees are. Maybe Western Union is cheaper. A good alternative is to get a Bank of America account in the US and to gice your daughter the debit card. As a Bank of America customer you can withdraw money without fees at Deutsche Bank ATMs in Germany. You don't need to have a Deutsche Bank account for that.

Hope this helped