What upgrades affect car performance

I'm not sure if I understand the question correctly.

But, from my understanding, No. Once you steal car X and tune it, it becomes a unique car, if car X gets destroyed and you can't repair it then you have to steal car X again and tune it again.

The only exception you have is for character specific cars. Like Trevor's Jeep, Michael's Audi and Franklin's Dodge/Ford. If you apply upgrades to them cars and then you destroy them, they will re-spawn with the upgrades there.

So answering directly to the question: It will be stock setup.

Each character has a personal unique car. If lost, it will appear near the garage of his safehouse. Sometimes, it will be in the vicinity of the character, when you switch to him.

Any customizations made to it will be permanent and cannot be undone, unless you re-customize it.

At some point in the story...

Jimmy De Santa will "borrow" his father's personal car, at which point it will become unavailable until Jimmy brings it back.

Michael's car will be customized, so you might want to customize his car only after that event.

No matter what you do, you cannot permanently lose your car, and any and all customizations done to it is permanent. Do not be afraid to abuse your tuned personal car as a cannonball, and don't be afraid of losing it.
Basically, tuning your personal car is a safer investment than tuning any other car.