The input ground should be tied to the ground on the input signal coming from your source to the amp. If the power supply is in the same case as the amp then this ground should be isolated from the chassis because the AC earth ground should be tied to chassis for safety reasons and you want to isolate the signal ground from AC earth ground. If the power supply is in a separate chassis then the input signal ground should be tied to chassis ground, but power supply ground should be isolated from chassis ground. Output ground should go to the ground connector on you headphone jack and should be isolated from chassis ground in all cases. For a TRS connector the ground should go to the 'S' connector.
By the way, the word is grateful, not great full.