The A9 you mentioned is definitely not a good idea. That autobahn is far too busy.
But I would suggest the A95 (Munich to Garmisch), because there are zones there where there is no speed limit. But please avoid weekends, otherwise you'll be stuck in traffic with everyone else driving to Garmisch. If you're planning on doing something like that, then do it during the middle of the day on a weekday. Along the route, apart from the final stop in Garmisch, there are a few places worth stopping. For example, Starnberg on Lake Starnberg (a coffee by the lake or a boat ride is always a good idea), Iffeldorf on the Osterseen (a very pretty little village on another lake), and not to forget 'The Blue Land' around Lake Kochel.
In addition, you are slowly (or quickly... it's up to you) getting closer to the mountains and therefore the scenery is becoming more and more picturesque.
The A95 begins in Munich at the Luise-Kiesselbach-Platz, so there's no classic autobahn ramp - you turn right or left from an ordinary road (depending on which direction you come from) and suddenly you are on the autobahn. The stretch up to Starnberg feels a bit like a normal road, as there are strict speed limits. So please pay close attention to the signs, as there are speed controls there.
Since I like driving fast myself, I can understand why you're looking forward to a day like this. However, as already has been mentioned, it's really advisable to memorize the signs and the rules, like 'drive on the right side except you want to overtake on the left side' (Rechtsfahrgebot). Especially on this autobahn, I've often seen one of the rich Starnberg dudes want to use his Ferrari as a race car in the left lane all the way to Garmisch, but some other drivers didn't understand that the left lane isn't for a leisurely Sunday drive :-)
Since there are often construction sites on German autobahn, I recommend checking them on google beforehand so you won't be surprised. The autobahn is usually still passable, but there are more speed limits due to the construction.