You are much better to purchase there. Once you purchase your Jagdschein and Waffenbesitzkarte, you could have your guns mailed to the APO/FPO address, but you would be required to send them to Koln for proofing and that runs 80+ Euro per gun. Here are the steps towards becoming a gun owner and hunter in the Heidelberg area.
1. Seek out a German Hunting Course at the R&G Club
2. While waiting for that, rent a shotgun and buy a case of steel shotshells (required on R&G ranges)
3. Start shooting Trap and Skeet
4. Doing that, you will soon meet a man named Dom Knoll
5. Become his friend by shooting at the "beer bird" every time he's around
6. He won't miss so you will probably be buying the pitcher afterwards
7. Keep doing that and a few weeks after you get your Jagdschein, he'll take you hunting
Dom is a retired Army NCO and takes good care of those within his circle of friends. Mention my name and he may even do you better than that by introducing you to Richard.
If that happens, you will be set my friend.
Thanks, Dinny