The German firearms laws are a little unusual if you havent been there before. I have German civvy friends and ex service mates who hold jagdschein and are active in the hunting scene. It also is open to anyone who can afford the fees. General sport shooting and historical arms etc is a different kettle of fish but there are supposed to be new EU wide regs regarding arms and civilian ownership coming into force soon. I wouldnt worry though as they would mean a relaxation here and a some severe changes in France. It wont happen.
If you want to hunt to need to do a course and pass an exam to get a hunting license, you can then purchase rifles (and pistols) but will of course have to have somewhere to hunt.
For target shooting it depends what disciplines you want to shoot, and you should join a club that specifically offers those disciplines. After a probation period you take a course (16hrs) in general weapons knowledge and German law, followed by a 70 question exam in German and a practical handling test. With the course pass certificate, a log book showing at least 18 visits in a year at a range, shooting club membership and sponsorship of a club official, you can apply to the Ordungsamt for a Waffenbesitzkarte and permission to purchase a weapon for a specific discipline offered by your club.