Banks

The banking system in EU countries is regulated under one framework. However, there are slight differences from country to country and it is most convenient to have as a primary account a German bank. It will provide you with German IBAN, EC-Karte (a german banking card, which is widely accepted in government offices, local shops, etc), a German bank account is protected by German law and the bank itself has to follow German laws (which usually have better customer and privacy protection than elsewhere).

Girokonto

This is just a german name for your usual checking account. Usually this is the cheapest, basic option, which comes with a free EC-Karte.

Card types

There are two widely used card types in Germany. National EC-Karte and worldwide Visa/Mastercard credit cards. EC-Karte is a debit card which is tied to your checking account, mostly accepted only inside Germany. By default, it's not possible to use online, but there are services which allow that option. However, this card is widely accepted within Germany and heavily used by government offices. Most of the times, it comes free of charge with the checking account.

Credit cards are typical Visa/Mastercard, which are accepted world-wide and can be used online without hassle. Most of the time, German banks charge a fee for issuing or maintenance of such cards. The tip here is to use online banks, which most of the time don't charge you for having a credit card.

Bank types

There are Online banks (Direktbanken) and traditional banks (Filialbanken). Online banks don't have a physical office, but usually provide a better experience when it comes to apps, websites, english-speaking support, etc. Traditional banks are favoured due to their reputation, size and stability.

Requirements

Travel Passport
Registration in Germany (if you don't have an official registration, you can try to use company address)
Long-term Visa or other document proving your legal status in Germany
(optional) A work contract. It's especially useful if you lack certain documents, like registration

This list is by no means exhaustive and you need to pay attention and read documents carefully, when choosing a bank.

Offline banks

At this point, most of the mainstream offline banks have an online-banking and mobile apps. However, they generally still lag behind online-only banks in terms of user experience.

Commerzbank

In the TOP 5 banks of Germany by asset size
Both offline and online
Good app with English language
Support speaks English
Option to have a free basic girokonto (conditions apply)
There is a 50 € bonus when opening an account (conditions apply)
Options to invest

Use this code to get a bonus: MAKVQ7

More info about opening account. Pay attention to conditions, as they change over time.

Deutsche Bank

The biggest bank in Germany
Both offline and online
Good app with English language
Support speaks English

Postbank

Both offline and online
Only German

Sparkasse

Both offline and online
Only German
The most widespread among Germans
One of the most annoying banks to use, due to various branches which not always connect with each other. So you might end up in a situation where you need to go specifically to your branch to edit your address or something like this.