Hi, I've researched this question and the only kind of meat that Muslims are not allowed to eat under any circumstances is pork. Other types of meat are OK as long as the animal has been slaughtered correctly, in the halal way.
Here is some information on requirements for halal slaughter (please be warned that some users may find this content upsetting): http://halalcertification.ie/halal/islamic-method-of-slaughtering/
It is possible to buy certified halal meat in Turkish and Arabic supermarkets. Here is a list of halal shops in Germany:
(On a PC, you should be able to use the Find function (Ctrl+F) to search for your city in this list).