Tune would be first mod for performance, cold air intake for sound, among a plethora of other mods that can be done once the vehicle is tuned. Also, welcome! Hope your LTZ treats you well.
Common issues: failed waterpump (covered by itself under an extended warranty), PCV system issues, coil packs tend to not always last very long, piston failures (less common, but possible), failed turbos (also less common). If any electrical gremlins pop up, make sure you inquire that they check your negative battery cable, there's a service bulletin for that to be replaced for free. Other than that, the car doesn't really have electrical issues or transmission issues (as long as you change your trans fluid when you're supposed to). If you notice the car running rough or slow in hot weather, use higher octane gas, it's a turbo vehicle with multiple fuel trim maps and runs much better on 91-93 octane.
