Sensible advice. An MX-5 as Fox says will be awful on the Autobahn and it's not that quick. German saloons are designed for the Autobahn, Japanese sports cars are not.Unrestricted autobahns are great fun, for about 5 minutes. Driving consistently above 200km/h is near impossible. Road works, noise restrictions (especially at night) and traffic means that 170/180km/h is sensible, 240+ for any stretch of time is ridiculously dangerous imho. It takes a remarkable amount of concentration at speed and so I would not recommend it at night. On 3 lanes of traffic trucks are usually no the main issue but grandpa/grandma in a honda jazz who decide to pull out from behind the truck at 100km/h. You can accelerate like a loon though which is fun and on good stretches hit your vmax if you wish to donate all your money to petrol stations. FYI if not obvious cruising at 200km/h takes significant amounts of petrol.
Imho, get a track day (or even autobahn to the ring?) and/or find some nice mountain passes! Lake district for example has way funner roads you can go on and not break the speed limit (although well into silly territory!). If determined to go to germany (which has lovely areas), go to the alps, you can do autobahns & mountain passes. Going to germany for just this seems like a waste.
Since apparently we must state our experience in these threads now.... I live in Munich about 1km from the A8 entrance and own a car that can go 250km/h and a bike that can do 260+ km/h (never hit vmax on bike, it gets way too scary). I regularly avoid the A8 and take the country roads to get to the alps because of traffic and because it's boring.
FWIW, there's a stretch of the A1 between Cologne and Hamm that's good fun as it's hilly and twisty, but only if you ignore the 120 limits and go at night. During the day it's too busy so you'd be doing it at night, which I wouldn't recommend if you haven't done it before.
Doing 200km/h+ up and down the hills and tight corners is risky but it's extremely good fun in a balanced, RWD car, but I suspect a track would be a more responsible thing to do.