After some online research about what different banks can offer me, I decided to choose DKB, it is a online bank free of charge and you can also take out money at any ATM world wide. Here you can read about different prices and also follow instructions, step by step, how to apply for a bank account. The list is not complete up to date since the guide was made in 2011, some changes has been made of DKB’s interface.
For Health insurance (Krankenkasse), I choose AOK Bayern. I got some suggestions of Health Insurances from the economy department at my work and then I asked a friend I have in München and he had AOK Bayern and he thought that it was no big difference in terms of what services they offer.