I've had 3 C6s: 06 paddle shift coupe, 08 stick shift vert and a 13 stick shift vert.
The 08 gave me the most trouble but it was all handled under warranty. I drove it for over 4 years.
The clutch pedal stuck to the floor once early in life. Repaired and had no more trouble from it.
The 06 was trouble free. This being the first of the 6-sp paddle shift transmission, it didn't shift when I thought it should using the paddles. Later paddle shift cars got better programming and work well. My wife drove it as a daily driver from 06 to 11.
The 13 is still in the garage and has been trouble free.
Corvette parts and labor can be high. Tires are costly. Used cars do need routine maintenance. Be prepared for that.