You need to get a German checking account (Girokonto) as soon as possible. For example to pay your rent for an apartment landlords expect the money to be transferred to their bank account every month. Also for utilities (water, electricity, gas, phone) you need a German bank account where the companies can deduct the money from. No sending checks around in Germany.

Large bank groups are:
Sparkasse
Volksbank
Postbank
Commerzbank
Deutsche Bank

Another difference to the US is who pays the realtor when looking for an apartment. The one who looks for the apartment pays the fee not the one who offers the apartment
.