The I-551 passport stamp is something you get only BEFORE you have the physical green card, not after the green card has arrived. The purpose of the I-551 passport stamp is to give you something you can use to prove your permanent resident status after your green card is approved and while you're waiting for the physical green card to arrive. So once you have received the physical green card, there is no reason to get the I-551 stamp and they won't give it to you unless your card is lost/expired and you've applied for renewal/replacement.
If you interviewed for the green card at a consulate and entered the US with an immigrant visa, you would already have the I-551 stamp. If you applied for the green card through adjustment of status (I-485) there is normally no need to ever get the passport stamp unless they take an unusually long time after approval to deliver the physical green card.
As far as the SS card is concerned, check if it has wording like "not valid for employment without DHS authorization". If it doesn't have that wording, keep it as is. If it has that wording, visit the SSA office with your GC to apply for a new card without the restrictive wording.