Sounds as confirmation for actions in the menu are a common way to
1. provide feedback
2. immerse the player
These sounds must not be as loud as they would be in-game, so quick menu-users can enjoy them even if they overlap.
I would suggest a "wroom!" motor sound for 'forward' actions and a breaks-squeak or tool or simple metal "dun" sound for 'back' actions (ESC).
There could be another sound for 'selection' actions (switching between level pages or cars). The 'change gears' sound from the game could be used.
The last action before shutting down the game should not have a sound attached, as it would be either wasted effort or it might force the game to wait until the sound has been played before shutdown.
Should there be a in-game/pause menu, the 'return to in-game' action should probably have no sound either.