If you want to try out driving on the German autobahn, the A2 BER-HAJ is certainly a route to try out. Its a completely rebuilt track, with no remnants of the old pre war GDR tracks. Its seems there is no construction planned either: http://www.bmvbs.de/bisliste.htm?bab=2

As far as an American driving on German roads is concerned, please inform yourself first. As there are many many servicemen on German roads, the US Armed Forces have many directives and advice websites. This (non USAF) is a good one: http://www.gettingaroundgermany.info/regeln.shtml , especially the Autobahn section.

So rent a Hertz/Europcar/Sixt car, pick a nice time to drive and enjoy the ride (please don't even think about sticking to 120, you will slow down the flow of traffic!)