There are many track car rental options. From a Suzuki swift for 99euro usually goes for 300 with gas and lap tolls to 911gt3s depends on your budget. Book early for the lower budget cars.
As far as rental cars, well I've taken them. The cars i had weren't the fastest (diesel: bmw 1series, skoda wagon, a4 wagon). Usually 2 laps back to back then a break. Just remove the lil Avis sticker off the back glass so that it's not 100% apparent. They check for dings/dents but I never noticed them checking the tires. It is a 2 hr drive to Frankfurt, perhaps I wore through enough of the pitted treads. I bet it was mostly cause I didn't rent an M3 or an other exclusive cars. The M3 are a bit pricey and come with a 200km limit I think per rental period.
The short 1-2hr days are pointless unless you get there 1hr+ before. Lines develop out to Nurburg. The prob is as mentioned any accident can shut the track down.
Hope this helps.
2011 M3 Dakar Yellow-Black Leather-Comp Pkg-DCT-Akra Evo-AP BBK Front-VOLK RE30/BBS GT4 18x10" Square
1995 M3 Boston Green - Chipped - Ground Control Coilovers - APEX ARC8
Past: 2005 Porsche Boxster S-Silver-6spd-Fabspeed Exhaust