To be accurate he wanted revenge for his mother's death, and to find out who did so he could wrought vengeance on them specifically. He holds a grudge for the imperial family because they would endanger him and Nunnally, thus is why he kills them. He also kills them for other reasons, being enemy commanders, being a liable threat, etc etc...
Zero Requiem was conjured up from Lelouch because he didn't feel much willingness to live after his little sister 'died' and his knights betrayed him. He had no one to turn to but a neutral geass witch and a knight that wanted him dead.
He wanted an escape, so he placed himself on the throne and named himself emperor so he could rule the world for a brief moment before perishing in Zero Requiem, as becoming emperor was also a way to lure out Schneizel and his benefactors so he could remove them as well.
He wanted peace, for himself and for the world. He would 'shed so much blood the name of the massacre princess would be forgotten/washed away." being a jab at what he was doing and what his intentions were.
He wanted to own up to his crimes, so he committed them more, he had a death wish and so forth.
To be lessen the explanation, it went like this
Suzaku wanted to die more then anything else, so his punishment for his crimes were to live as Zero - the messiah he held in contempt.
Lelouch wanted to live in the world he would make for Nunnally, so his punishment for his crimes was to die in the process of making a new world.
Someone could do a better job, just ill luck for you to get me telling you
