Read the terms and conditions and see if you still feel rentals is a good way to go...
http://www.rent-racecar.de/english/crg/index.htm
In simple terms, as long as you've done nothing stupid, and you've taken out comprehensive insurance (no costs quoted on the site, but likely to cost a HUGE amount of money) you're only liable for the excess in the event of you being involved in an accident (which ranges from €5.000 for the Suzuki Swift Sport to €17.000 for the Porsche 911 Carrera 996 and BMW M3 E92). I'm not 100% sure as the language in the terms is a bit confusing, but you may also be liable for the cost of recoverey and damage assesment, and the loss of rental income whilst the car is off the road even when you have comprehensive insurance.
Without the comprehensive insurance you're pretty much liable for
everything other than any injury you may cause to another car or person whilst driving as long as you're not doing something stupid - if you are doing something stupid or negligent you're liable for those things too).
On top of the costs above, you also need to consider the costs the track owner will impose on you...
* Base fee for attendance of armco truck: €150
Removing damaged armco: €10/metre (x2 or x3 or x4 for multiple-height sections)
Replacement armco: €31/metre (x2 or x3 for double/triple height)
Removing damaged armco posts: €5.10 each
Replacing armco post: €39 each
Safety car attendance: €82 per 30 mins (car + 2 people)
* Circuit closure: €1,350 per hour
Recovery truck: €190 (inc VAT)
Hospital stay & air ambulance: A lot, but should be covered if you have good travel insurance
Everything except the recovery truck is then subject to 19% VAT.
Imakuni is absolutely spot on... get yourself a cheapish, but mechanically sound FWD hatch and drive well within your abilities. Also, try and get yourself on a proper organised track day rather than a public session.