When researching the crusades I've often came across the notion that some crusaders wanted to conquer Egypt, which makes sense considering it would be important to securing Jerusalem.
What would be the best opportunity for the crusaders to successfully do this if at all, how would this kingdom be administrated, what would it's relationship with the Byzantines be like, which of the Italian city states would be influential, which areas would be vital towards its long-term survival, and what would it's culture be like?