The end of a meal is often when everyone relaxes and the serving dishes are forgotten. Having suitable containers ready makes storage a smaller interruption.
Set aside clean shallow containers before guests arrive if you expect leftovers. After eating, portion and refrigerate perishable food promptly according to applicable guidance. Label it so tomorrow's cook knows what it is and when it was made.
If sending food home, consider the guest's travel time and cooling arrangements. A container alone is not a safe transport plan. Do not send questionable leftovers simply to avoid throwing them away.
Keep crisp toppings and wet dishes separate when practical. That helps texture later, but safe handling comes first. A meal can end warmly without leaving every bowl on the table for the rest of the evening.
Further reading: FDA: storing food safely.